Full CV
(Last updated: July 24, 2024)
TOBB Economics and Technology University,
Department of Mathematics
Söğütözü TR-06530, Ankara, Turkey
E-Mail: oduman@etu.edu.tr; okitayduman@gmail.com
Website: http://oduman.etu.edu.tr/
Education:
Ph.D.: Ankara University, Department of Mathematics (1998-2003; advisor: Prof. Dr. Cihan Orhan)
M. Sc.: Ankara University, Department of Mathematics (1996-1998; advisor: Prof. Dr. Kaya Özkın)
B. Sc.: Ankara University, Department of Mathematics (1992-1996)
Academic Employment:
Full Professor: TOBB ETU, Ankara, Turkey, 2010-present
Visiting Scholar: University of Central Florida (UCF), Orlando, FL, USA, 2015
Associate Professor: TOBB ETU, Ankara, Turkey, 2005-2010
Assistant Professor: TOBB ETU, Ankara, Turkey, 2004-2005
Research Assistant: Ankara University, , Ankara, Turkey, 1997-2003
Research Areas:
Approximation theory and its applications
Summability theory and its applications
Awards, Honors, and Grants:
Included in the list of "The World's Most Influential Scientists", Stanford University - Elsevier, October, 2023.
Elected as an "Principle Member" by TUBA (The Turkish Academy of Sciences), December 2020.
"Best Organizer Award" in 2019 IEEE 10th International Conference on Mechanical and Aerospace Engineering (ICMAE 2019), Brussels - Belgium, July 22-25, 2019.
TUBITAK Grant, University of Central Florida, USA, 2015.
Elected as an "Associate Member" by TUBA (The Turkish Academy of Sciences), 2012 - 2020.
Research Reward Dedicated to "Professor Masatoschi Gündüz Ikeda", Mathematics Foundation of Turkey, 2005.
Editorial:
Demonstratio Mathematica (Member of Editorial Board, SCI-Q1)
Communications - Fac. Sci. Univ. Ank. Series A1: Math. Stat. (Member of Area Editors, ESCI)
Journal of Mathematical Analysis (Member of Editorial Board, ESCI)
Journal of Computational Analysis and Applications (Member of Editorial Board)
Turkish Journal of Mathematics (Guest Editor, SCI-Q3)
Professional Memberships:
The Mathematical Association of America - MAA (2006-...)
American Mathematical Society - AMS (2004-...)
Refereeing:
Reviewer: AMS-Mathematical Reviews
J. Approx. Theory (SCI)
J. Math. Anal. Appl. (SCI)
J. Comput. Appl. Math. (SCI)
Appl. Math. Lett. (SCI)
Chaos, Solitons & Frantals (SCI)
Nonlinear Dynamics (SCI)
Comput. Math. Appl. (SCI)
Fuzzy Sets and Systems (SCI)
Taiwanese J. Math. (SCI)
Internat. J. Bifur. Chaos (SCI)
J. Comput. Physics (SCI)
Math. Inequal. Appl. (SCI-Expanded)
Math. Slovaca (SCI-Expanded)
Math. Comput. Modelling (SCI-Expanded)
Rocky Mountain J. Math. (SCI-Expanded)
Studia Sci. Math. Hungar. (SCI-Expanded)
Positivity (SCI-Expanded)
Publ. Math. Debrecen (SCI-Expanded)
Miskolc Math. Notes (SCI-Expanded)
Information Sciences (SCI-Expanded)
Appl. Math. Comput (SCI-Expanded)
J. Inequal. Appl. (SCI-Expanded)
Math. Model. Anal. (SCI-Expanded)
Turkish J. Math. (SCI-Expanded)
Iran. J. Fuzzy Syst. (SCI-Expanded)
Hacettepe J. Math. Stat. (SCI-Expanded)
Math. Commun. (SCI-Expanded)
Discrete Dynam Nat. Soc. (SCI-Expanded)
Indian J. Pure and Appl. Math. (SCI-Expanded)
J. Appl. Math. (AMS-MR)
Acta Math. Appl. Sinica (AMS-MR)
Internat. J. Math. Math. Sci. (AMS-MR)
Comput. Lett. (AMS-MR)
J. Math. Control Sci. Appl. (AMS-MR)
Kyungpook Math. J. (AMS-MR)
Assian Bull. Math. (AMS-MR)
Abst. Appl. Anal. (AMS-MR)
J. Appl. Anal. (AMS-MR)
Pakistan J. Statist. (AMS-MR)
Appl. Math. Inf. Sci. (AMS-MR)
Demonstratio Math. (AMS-MR)
J. Reliability Stat. Stud. (AMS-MR)
Int. J. Biomath. (AMS-MR)
Appl. Math. Inform. Sci. (AMS-MR)
Selcuk J. Appl. Math. (AMS-MR)
Gazi Univ. J. Sci. (AMS-MR)
Commun. Fac. Sci. Univ. Ankara (AMS-MR)
Duties in Projects and Programs:
Principle Investigator: "Mentorship Program", TUBITAK 2248 Program, 26 May 2023 - 26 May 2028.
Principle Investigator: "Grant Program for Scientific Training", TUBITAK 2237-A Program, December 2022 and June 2023.
Advisor: "Application the Bell-type summability method to nonlinear operators and image processing", TUBITAK 3501 Project, No: 119F262, 15 March 2020 - 15 March 2022 (Principle investigator: İsmail Aslan).
Scholarship: "International Postdoctoral Research Fellowship Program", TUBITAK 2219 Program, University of Central Florida, USA, 01 July 2015 - 01 September 2015.
Principle Investigator: "Statistical approximation of linear operators by means of summability theory", TUBITAK 1002 Project, No: 108T229, 15 May 2008 - 15 May 2009.
Scholarship: "Statistically Convergent Function Sequences", TUBITAK BAYG Project, 15 September 1998 - 15 September 2002 (Principle investigator: Cihan Orhan).
Thesis Supervised:
Meryem Ece Alemdar (TOBB ETU, Ph.D., 2020 - …)
Can Türkün (TOBB ETU, Ph.D., 2020)
Türkan Yeliz Gökçer (TOBB ETU, Ph.D., 2020)
Meryem Ece Alemdar (TOBB ETU, M.Sc., 2020)
İsmail Aslan (TOBB ETU, Ph.D., 2019)
Ceylan Turan (TOBB ETU, Ph.D., 2017)
Türkan Yeliz Gökçer (TOBB ETU, M.Sc., 2016)
Engin Sarı (TOBB ETU, M.Sc., 2015)
İsmail Aslan (TOBB ETU, M.Sc., 2014)
Nisa Küçük (TOBB ETU, M.Sc., 2014)
Ceylan Turan (TOBB ETU, M.Sc., 2012)
Alperen Ali Ergür (TOBB ETU, M.Sc., 2011)
Merve Kester (TOBB ETU, M.Sc., 2011)
Administrative Duties in the University:
Dean of Faculty of Arts and Sciences at TOBB ETU (2020-…)
Senate Member at TOBB ETU (2020-...)
Chair of Department of Mathematics at TOBB ETU (2015-...)
Vice Dean of Faculty of Arts and Sciences at TOBB ETU (2013-2020)
Vice Chair of Department of Mathematics at TOBB ETU (2006-2008)
Duties in Conferences:
Member of International Scientific Committee: "4th International Conference on Artificial Intelligence and Applied Mathematics in Engineering - ICAIAME 2022", Baku, Azerbaijan, May 20-22, 2022.
Member of International Scientific Committee: "3rd International Conference on Artificial Intelligence and Applied Mathematics in Engineering - ICAIAME 2021", Antalya, Türkiye, October 1-3, 2021.
Minisymposium Co-Organizer: “Approximation Theory and Special Functions - 7th series” in the International Conference: "The 7th International Conference on Recent Advances in Pure and Applied Mathematics - ICRAPAM 2020", Muğla, Türkiye, September 25-28, 2020.
Member of International Scientific Committee: "2nd International Conference on Artificial Intelligence and Applied Mathematics in Engineering - ICAIAME 2020", Antalya, Türkiye, October 9-11, 2020.
Minisymposium Co-Organizer: “Approximation Theory and Special Functions - 6th series” in the International Conference: "The 8th International Conference on Pure and Applied Mathematics - ICPAM 2019", Brussels, Belgium, July 22-25, 2019.
Member of Organizing Committee: "14th Ankara Matematics Days - AMG 2019", Gazi University, Ankara, Türkiye, June 28-29, 2019.
Member of International Scientific Committee: "1st International Conference on Artificial Intelligence and Applied Mathematics in Engineering - ICAIAME 2019", Antalya, Türkiye, April 20-22, 2019.
Minisymposium Co-Organizer: “Approximation Theory and Special Functions - 5th series” in the International Conference: "The 7th International Conference on Pure and Applied Mathematics - ICPAM 2018", Eötvös Lorand University, Budapest, Hungary, July 10-13, 2018.
Conference Chair: "13th Ankara University, Ankara, Turkey - AMG 2018", TOBB ETU, Ankara, Türkiye, April 27-28, 2018.
Minisymposium Co-Organizer: “Approximation Theory and Special Functions - 4th series” in the International Conference: "The International Society for Analysis, its Applications and Computation - ISAAC 2017", Linnaeus University, Vaxjo, Sweden, August 14-18, 2017.
Member of Organizing Committee: "12th Ankara Matematics Days - AMG2017", Hacettepe University, Ankara, Türkiye, May 25-26, 2017.
Member of International Scientific Committee: "International Workshop on Mathematical Methods in Engineering - MME 2017", Çankaya University, Ankara, Türkiye, April 27-29, 2017.
Minisymposium Co-Organizer: “Approximation Theory and Special Functions - 3rd series” in the International Conference: "Emerging Trends in Applied Mathematics and Mechanics – ETAMM 2016", Perpignan, France, May 30 - June 03, 2016.
Member of Organizing Committee: "11th Ankara Matematics Days - AMG 2016", Ankara University, Ankara, Türkiye, May 26-27, 2016.
Member of Scientific Committee: "10th Ankara Matematics Days - AMG 2015", Middle East Technical University, Ankara, Türkiye, June 11-12, 2015.
Conference Co-Chair: "3rd International Conference on Applied Mathematics and Approximation Theory - AMAT 2015", TOBB ETU, Ankara, Türkiye, May 28-31, 2015.
Minisymposium Co-Organizer: "Approximation Theory and Special Functions - 2nd Series" within "International Conference: Mathematics Days in Sofia - MDS 2014", Sofia, Bulgaria, July 07-10, 2014.
Member of Scientific Committee: "9th Ankara Matematics Days - AMG 2014", Atılım University, Ankara, Türkiye, June 12-13, 2014.
Minisymposium Co-Organizer: "Approximation Theory and Special Functions - 1st Series" within "11th International Conference of Numerical Analysis and Applied Mathematics - ICNAAM 2013", Rhodes Island - Greece, September 21-27, 2013.
Member of Scientific Committee: "8th Ankara Matematics Days - AMG 2013", Hacettepe University, Ankara, Türkiye, June 13-14, 2013.
Member of Scientific Committee: "7th Ankara Matematics Days - AMG 2012", Bilkent University, Ankara, Türkiye, May 31 - June 01, 2012.
Conference Chair: "International Conference on Applied Mathematics and Approximation Theory - AMAT 2012", TOBB ETU, Ankara, Türkiye, May 17-20, 2012.
Conference Chair: "5th Ankara University, Ankara, Turkey - AMG 2010", TOBB ETU, Ankara, Türkiye, June 03-04, 2010.
Member of Scientific Committee: "International Workshop on New Trends in Science and Technology", Cankaya University, Ankara, Türkiye, November 03-04, 2008.
Member of Organizing Committee: "1. Üstün Yetenekli Çocuklan Kongresi", İstanbul, Türkiye, September 23-25, 2004.
Courses Taught:
Approximation Theory (graduate)
Functions Theory (graduate)
Real Analysis I (graduate)
Real Analysis II (graduate)
Introduction to Approximation Theory (undergraduate)
Functional Analysis (undergraduate)
Advanced Analysis I-II (undergraduate)
Complex Functions Theory I-II (undergraduate)
Measure Theory (undergraduate)
Complex Analysis (undergraduate)
Introduction to Analysis I-II (undergraduate)
Calculus I-II (undergraduate)
Invited Talks:
O. Duman, Yaklaşım Teorisinde Son Gelişmeler: Modifiye Shepard Yaklaşımı, Hacettepe Üniversitesi, Ankara, Türkiye, 24 Nisan 2024.
O. Duman, Doğada Matematik, "Evreni Anlama Sanatı: Temel Bilimler Konferansı", Selçuk Üniversitesi, Konya, Türkiye, 11-12 Ekim, 2022.
O. Duman, Kompleks Shepard operatörleri ve uygulamaları, "Yaklaşımlar Teorisi ve Uygulamaları Çalıştayı", Hacettepe Üniversitesi, Ankara, Türkiye, 4 Mart 2022.
O. Duman, Lineer olmayan operatörlerle fonksiyonlara yaklaşım ve toplanabilme, Mersin Üniversitesi, Matematik Bölümü, Mersin, Türkiye, 26 Ekim 2018.
O. Duman, Summability methods in singular approximation, Çankaya University, Department of Mathematics, Ankara, Türkiye, November 09, 2016.
O. Duman, Iraksak seriler, toplanabilme ve Hardy, Doğu Akdeniz Üniversitesi, Matematik Bölümü, Gazimagosa, KKTC, 20 Mart 2015.
O. Duman, Toplanabilme teorisinin yaklaşımlar teorisi üzerindeki etkileri, Anadolu Üniversitesi, Matematik Bölümü, Eskişehir, Türkiye, 23 Mayıs 2013.
O. Duman, Yaklaşımlar teorisinde yeni yaklaşım tekniklerinin ihtiyacı, TÜBA Konferansı, Karabük Üniversitesi, Matematik Bölümü, Karabük, Türkiye, 26 Nisan 2013.
O. Duman, Convergence methods in approximation theory, Bilkent University, Department of Mathematics, Ankara, Türkiye, November 16, 2011.
O. Duman, Recent developments in approximation theory, TOBB Economics and Technology University, Department of Mathematics, Ankara, Türkiye, October 12, 2011.
O. Duman, Recent improvements on statistical approximation theory, Izmir University of Economics, Department of Mathematics, İzmir, Türkiye, April 26, 2010.
O. Duman, Uniform statistical approximation by double Gauss-Weierstrass singular integral operators, Gazi University, Department of Mathematics, Ankara, Türkiye, November 06, 2009.
O. Duman, A Baskakov type generalization of statistical Korovkin theory, Ankara University, Department of Mathematics, Ankara, Türkiye, April 15, 2009.
O. Duman, Statistical convergence and Korovkin-type approximation theory, "Mathematical Analysis, Differential Equations and Their Applications", Eastern Mediterranean University, Famagusta-North Cyprus, September 12-15, 2008.
O. Duman, On relaxing the positivity condition of linear operators in statistical Korovkin-type approximations, Ankara University, Department of Mathematics, Ankara, Türkiye, April 30, 2008.
O. Duman, Allee effects on population Dynamics, Çankaya University, Nano-Science and Research Center, Ankara, Türkiye, December 27, 2007.
O. Duman, Approximation properties of positive linear operators, Çankaya University, Department of Mathematics and Computer Science, Ankara, Türkiye, December 15, 2006.
O. Duman, Statistical approximation by positive linear operators, Middle East Technical University, Department of Mathematics, Ankara, Türkiye, March 24, 2005.
O. Duman, A-statistical convergence of approximating operators, Ankara University, Department of Mathematics, Ankara, Türkiye, May 20, 2004.
International/National Contributed Talks:
M. E. Alemdar and O. Duman, Regular summability methods in the approximation by Bernstein-Chlodovsky type operators, "The 7th International Conference on Recent Advances in Pure and Applied Mathematics - ICRAPAM 2020", Muğla, Türkiye, September 25-28, 2020.
T. Y. Gökçer and O. Duman, Approximation theorems for max-min operators via summability methods, "The 7th International Conference on Recent Advances in Pure and Applied Mathematics - ICRAPAM 2020", Muğla, Türkiye, September 25-28, 2020.
T. Y. Gökçer and O. Duman, General approach for approximation by max-min operators, "The 8th International Conference on Pure and Applied Mathematics - ICPAM 2019", Brussels, Belgium, July 22-25, 2019.
M. E. Alemdar and O. Duman, On the approximation by Bernstein-Chlodovsky type operators, "The 8th International Conference on Pure and Applied Mathematics - ICPAM 2019", Brussels, Belgium, July 22-25, 2019.
İ. Aslan and O. Duman, Summability method in the approximation by nonlinear integral operators in N-dimension BV-space, "The 7th International Conference on Pure and Applied Mathematics - ICPAM 2018", Eötvös Lorand University, Budapest, Hungary, July 10-13, 2018.
T. Y. Gökçer and O. Duman, Some convergence methods on max-min operators, "The 7th International Conference on Pure and Applied Mathematics - ICPAM 2018", Eötvös Lorand University, Budapest, Hungary, July 10-13, 2018.
İ. Aslan and O. Duman, Approximation by nonlinear integral operators with the help of summation methods, "The International Society for Analysis, its Applications and Computation - ISAAC 2017", Linnaeus University, Vaxjo, Sweden, August 14-18, 2017.
T. Y. Gokcer and O. Duman, Some convergence methods on pseudo linear operators, "The International Society for Analysis, its Applications and Computation - ISAAC 2017", Linnaeus University, Vaxjo, Sweden, August 14-18, 2017.
C. Türkün and O. Duman, Neural network approximation in summation process, "The International Society for Analysis, its Applications and Computation - ISAAC 2017", Linnaeus University, Vaxjo, Sweden, August 14-18, 2017.
T. Y. Gokcer and O. Duman, On the approximation by max-min and max-product operators, "International Conference on Mathematics and Mathematics Education - ICMME 2017", Harran University, Şanlıurfa, Türkiye, May 11-13, 2017.
İ. Aslan and O. Duman, Summability process on the approximation by nonlinear integral operators of convolution type, "International Conference on Mathematics and Mathematics Education - ICMME 2017", Harran University, Şanlıurfa, Türkiye, May 11-13, 2017.
Y. Gokcer and O. Duman, Summation Process in Approximation by Nonlinear Operators, "Emerging Trends in Applied Mathematics and Mechanics – ETAMM 2016", Perpignan, France, May 30 - June 03, 2016.
C. Turan and O. Duman, Hardy Type Tauberian Condition on Time Scales, "Emerging Trends in Applied Mathematics and Mechanics – ETAMM 2016", Perpignan, France, May 30 - June 03, 2016.
İ. Aslan and O. Duman, A Generalized Version of the Korovkin Theory, "Emerging Trends in Applied Mathematics and Mechanics – ETAMM 2016", Perpignan, France, May 30 - June 03, 2016.
Y. Gokcer and O. Duman, Summation process by max-product operators, "3rd International Conference on Applied Mathematics and Approximation Theory - AMAT 2015", Ankara, Türkiye, May 28-31, 2015.
C. Turan and O. Duman, On convergence methods of functions defined on time scales, "International Conference on Recenet Developments in Pure and Applied Mathematics - ICRAPAM 2014", Antalya, Türkiye, November 06-09, 2014.
İ. Aslan and O. Duman, Application of summability process on Baskakov-type approximation theory, "International Conference on Recenet Developments in Pure and Applied Mathematics - ICRAPAM 2014", Antalya, Türkiye, November 06-09, 2014.
C. Turan and O. Duman, Recent developments on convergence methods on time scales, “International Conference: Mathematics Days in Sofia - MDS 2014", Sofia, Bulgaria, July 07-10, 2014.
İ. Aslan and O. Duman, Summability process on the Baskakov-type approximation theory, “International Conference: Mathematics Days in Sofia - MDS 2014", Sofia, Bulgaria, July 07-10, 2014.
N. Küçük and O. Duman, Summability methods in the weighted approximation to derivatives of functions, “International Conference: Mathematics Days in Sofia - MDS 2014", Sofia, Bulgaria, July 07-10, 2014.
C. Turan and O. Duman, Convergence methods on time scales, “11th International Conference of Numerical Analysis and Applied Mathematics – ICNAAM 2013", Rhodes, Greece, September 21-27, 2013.
O. Duman, Summability process by Mastoianni operators, “26^{th} National Mathematics Symposium”, Diyarbakır-Turkey, September 4-7, 2013.
C. Turan and O. Duman, Statistical convergence on time scales, “International Conference on Applied Mathematics and Approximation Theory – AMAT 2012”, TOBB ETU, Ankara, Türkiye, May 17-20, 2012.
O. Duman and E. Erkuş-Duman, Approximation by matrix-valued linear positive operators, “Conference on Matrix Analysis and its Applications – MAT TRIAD 2011, Tomar, Portugal, July 12-16, 2011.
G. A. Anastassiou and O. Duman, Statistical approximation by double Picard singular integral operators, “4th Ankara Mahematics Days”, METU, Ankara, Türkiye, June 04-05, 2009.
O. Duman, Stability analysis of population dynamics under Allee effects, “International Workshop on New Trends in Science and Technology”, Çankaya University, Ankara, Türkiye, November 03-04, 2008.
O. Duman, Statistical convergence and Korovkin-type approximation theory, “Mathematical Analysis, Differential Equations and Their Applications”, Eastern Mediterranean University, Famagusta-North Cyprus, September 12-15, 2008.
O. Duman, A new approach in obtaining a better estimation in the approximation by positive linear operators, “3rd Ankara Mahematics Days”, METU, Ankara University, Ankara, Türkiye, May 22-23, 2008.
O. Duman and E. Erkuş-Duman, Statistical approximation to continuous periodic functions by means of positive linear operators, “2nd Turkish World Mathematics Symposium”, Sakarya University, Sakarya, Türkiye, July 04-07, 2007.
O. Duman, Stability analysis of delay population dynamics under Allee effects, “TASSA Conference”, Yale University, New Haven, USA, March 24-25, 2007.
O. Duman and M. A. Özarslan, MKZ type positive linear operators providing a better error estimation, “19th National Mathematics Symposium”, Kütahya, Türkiye, August 22-25, 2006.
O. Duman and C. Orhan, Rates of A-statistical convergence of positive linear operators, “Fejer-Riesz Conference”, Eger, Hungary, June 09-13, 2005.
Citation Report (ISI Web of Science - Pablons):
Publications in web of science: 110
Sum of times cited: 1875
h-index: 25
Publications:
O. Duman, B. Della Vecchia and E. Erkus-Duman, Kantorovich version of vector-valued Shepard operators, Axioms 13 (2024), Paper No. 181, 12 pp.
O. Duman, Max-product Shepard operators based on multivariable Taylor polynomials, J. Comput. Appl. Math. 437 (2024), Paper No. 115456, 15 pp.
O. Duman and B. Della Vecchia, Vector-valued Shepard processes: Approximation with summability, Axioms, 12 (2023), Paper No. 1124, 16 pp.
C. Turan Yalçın and O. Duman, Regular integral transformations on time scales and generalized statistical convergence, Filomat 37 (2023), no. 12, 4017-4028.
O. Duman and B. Della Vecchia, Approximation to integrable functions by modified complex Shepard operators, J. Math. Anal. Appl. 512 (2022), no. 2, Paper No. 126161, 13 pp.
T. Y. Gökçer and O. Duman, Regular summability methods in the approximation by max-min operators, Fuzzy Sets Systems 426 (2022), 106-120.
O. Duman and B. Della Vecchia, Complex Shepard operators and their summability, Results Math. 76 (2021), no. 4, Paper No. 214, 19 pp.
M. E. Alemdar and O. Duman, General summability methods in the approximation by Bernstein-Chlodovsky operators, Numer. Funct. Anal. Optim. 42 (2021), no. 5, 497-509.
İ. Aslan and O. Duman, Nonlinear approximation in n-dimension with the help of summability methods, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 115 (2021), no. 3, paper no. 105, 27 pp.
O. Duman, Generalized Cesaro summability of Fourier series and its applications, Constr. Math. Anal. 4 (2021), no. 2, 135-144.
İ. Aslan and O. Duman, Characterization of absolute and uniform continuity, Hacettepe J. Math. Stat. 49 (2020), no. 5, 1550-1565.
O. Ocalan and O. Duman, Solutions to conjectures on a nonlinear recursive equation, Czechoslovak Math. J. 70 (2020), no. 3, 867-880.
T. Y. Gökçer and O. Duman, Approximation by max-min operators: A general theory and its applications, Fuzzy Sets Systems, 394 (2020), 146-161.
C. Turkun and O. Duman, Modified neural network operators and their convergence properties with summability methods, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 114 (2020), no. 3, paper no. 132, 18 pp.
İ. Aslan and O. Duman, Approximation by nonlinear operators via summability process, Math. Nachr. 293 (2020), no. 3, 430-448.
(Book chapter) O. Duman, Error estimation for approximate solutions of delay Volterra integral equations, in "Frontiers in Functional Equations and Analytic Inequalities", pp. 585-597, Springer Nature, Switzerland, 2019.
İ. Aslan and O. Duman, Summability on Mellin-type nonlinear integral operators, Integral Transform. Spec. Funct. 30 (2019), no. 6, 492-511.
O. Ocalan and O. Duman, On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences, Electron. J. Math. Anal. Appl. 7 (2019), no. 1, 102-115.
C. Turan and O. Duman, Hardy-type Tauberian conditions on time scales, Mediterr. J. Math. 15 (2018), no. 5, Art. 198, 12 pp.
C. Turan and O. Duman, Fundamental properties of statistical convergence and lacunary statistical convergence on time scales, Filomat, 31 (2017), no. 14, 4455-4467.
O. G. Atlihan, M. Unver and O. Duman, Korovkin theorems on weighted spaces: revisited, Periodica Math. Hungar. 75 (2017), no. 2, 201-209.
O. Duman, Singular approximation in polydiscs by summability process, Positivity 20 (2016), no. 3, 663-676.
(Book chapter) T. Y. Gökçer and O. Duman, Summation process by max-product operators, in "Computational Analysis", pp. 59-67, Springer Proceedings in Mathematics & Statistics, Springer, New York, 2016.
(Edited-book) G.A. Anastassiou and O. Duman (eds.), Computational Analysis, Springer Proceedings in Mathematics & Statistics, Springer, New York, 2016, 3396 p. ISBN 978-3-319-28441-5.
İ. Aslan and O. Duman, Summability process on the Baskakov-type approximation, Periodica Math. Hungar. 72 (2016), no. 2, 186-199.
(Book chapter) O. Duman, Nonlinear approximation: q-Bernstein operators of max-product kind, in "Intelligent Mathematics II: Applied Mathematics and Approximation Theory", pp. 33-56, Advances in Intelligent Systems and Computing, Vol. 441, Springer, Heidelberg, 2016.
(Edited-book) G.A. Anastassiou and O. Duman (eds.), Intelligent Mathematics II: Applied Mathematics and Approximation Theory, Advances in Intelligent Systems and Computing, Vol. 441, Springer, Heidelberg, 2016, 502 p. ISBN 978-3-319-30322-2.
M. A. Özarslan and O. Duman, Smoothness properties of modified Bernstein-Kantorovich operators, Numer. Funct. Anal. Optim. 37 (2016), no. 1, 92-105.
N. Küçük and O. Duman, Summability methods in weighted approximation to derivatives of functions, Serdica Math. J. 41 (2015), 355-368.
O. Duman, Summability process by Mastroianni operators and their generalizations, Mediterr. J. Math. 12 (2015), 21-35.
O. Duman, Nonlinear Bernstein-type operators providing a better error estimation, Miskolc. Math. Notes 15 (2014), no. 2, 393-400.
O. Duman, Summability process by singular operators, Publ. Math. Debrecen 85 (2014) 373-386.
(Edited-book) G.A. Anastassiou and O. Duman (eds.), Advances in Applied Mathematics and Approximation Theory, Springer Proceedings in Mathematics & Statistics, Vol. 41, Springer, New York, 2013, 486 pp. ISBN: 978-1-4614-6393-1.
C. Turan and O. Duman, Convergence methods on time scales, AIP Conf. Proc. 1558 (2013) 1120-1123.
(Book chapter) C. Turan and O. Duman, Statistical convergence on time scales and its characterizations, n "Advances in Applied Mathematics and Approximation Theory", pp. 57-71, Springer Proc. Math. Stat., vol. 41, Springer, New York, 2013.
A. A. Ergür and O. Duman, Generalization of statistical Korovkin theorems, J. Appl. Math. 2013, Article ID 187530, 5 pp.
Z. Ünal, M. A. Özarslan and O. Duman, Approximation properties of real and complex Post-Widder operators based on q-integers, Miskolc. Math. Notes 13 (2012) 581-603.
O. Duman and M. Kester, Statistical approximation by double Poisson-Cauchy singular integral operators, Results Math. 62 (2012) 53-65.
A. D. Gadjiev, O. Duman and A. M. Ghorbanalizadeh, Ideal convergence of k-positive linear operators, J. Funct. Spaces Appl. 2012, Article ID 178316, 12 pp.
(Monograph-book) G.A. Anastassiou and O. Duman, Towards Intelligent Modeling: Statistical Approximation Theory, Intelligent Systems Reference Library, Vol. 14, Springer, Berlin, 2011, 234 pp. ISBN: 978-3-642-19825-0.
O. Duman and E. Erkuş-Duman, Statistical Korovkin-type theory for matrix-valued functions, Studia Sci. Math. Hungar. 48 (2011) 489-508.
H. Aktuğlu, M. A. Özarslan and O. Duman, Matrix summability methods on the approximation of multivatiate q-MKZ operators, Bull. Malaysian Math. Sci. Soc. 34 (2011) 465-474.
A. Aral and O. Duman, A Voronovskaya-type formula for SMK operators via statistical convergence, Math. Slovaca 61 (2011) 235-244.
M. Burgin and O. Duman, Approximations by linear operators in spaces of fuzzy continuous functions, Positivity 15 (2011) 57-72.
M. A. Özarslan, O. Duman and N. I. Mahmudov, Local approximation properties of modified Baskakov operators, Results Math. 59 (2011) 1-11.
G. A. Anastassiou and O. Duman, Statistical Lp-convergence of double smooth Picard singular integral operators, J. Comput. Anal. Appl. 13 (2011) 167-187.
O. Duman and M. A. Özarslan, Global approximation results for modified Szasz-Mirakjan operators, Taiwanese J. Math. 15 (2011) 75-86.
G. A. Anastassiou and O. Duman, Statistical approximation by double complex Gauss-Weierstrass integral operators, Appl. Math. Lett. 24 (2011) 438-443.
E. Erkuş-Duman and O. Duman, Statistical approximation properties of high order operators constructed with the Chan-Chyan-Srivastava polynomials, Appl. Math. Comput. 218 (2011) 1927-1933.
M. Burgin and O. Duman, Approximate fuzzy continuity of functions, Internat. J. Fuzzy Syst. Appl. 1 (2011) 37-46.
O. Duman, Statistical fuzzy approximation to fuzzy differentiable functions by fuzzy linear operators, Hacettepe J. Math. Stat. 39 (2010) 497-514.
M. A. Özarslan and O. Duman, Local approximation behavior of modified SMK operators, Miskolc Math. Notes 11 (2010) 87-99.
O. Duman, Statistical convergence of max-product approximating operators, Turkish J. Math. 34 (2010) 501-514.
F. Dirik, O. Duman and K. Demirci, Approximation in statistical sense to B-continuous functions by positive linear operators, Studia Sci. Math. Hungar. 47 (2010) 289-298.
M. A. Özarslan and O. Duman, Global approximation properties of modified SMK operators, Filomat 24 (2010) 47-61.
S. Karakuş, K. Demirci and O. Duman, Statistical approximation by positive linear operators on modular spaces, Positivity 14 (2010) 312-334.
G. A. Anastassiou and O. Duman, Statistical convergence of double complex Picard integral operators, Appl. Math. Lett. 23 (2010) 852-858.
M. A. Özarslan, O. Duman and C. Kaanoğlu, Rates of convergence of certain King-type operators for functions with derivative of bounded variation, Math. Comput. Modelling 52 (2010) 334-345.
G. A. Anastassiou and O. Duman, Statistical Korovkin theory for multivariate stochastic processes, Stoch. Anal. Appl. 28 (2010) 648-661.
O. Duman, Fuzzy approximation based on statistical rates, Publ. Math. Debrecen 76 (2010) 453-463.
G. A. Anastassiou and O. Duman, Statistical Lp approximation by double Gauss-Weierstrass singular integral operators, Comput. Math. Appl. 59 (2010) 1985-1999.
O. Duman, M. A. Özarslan and E. Erkuş-Duman, Rates of ideal convergence for approximation operators, Mediterr. J. Math. 7 (2010) 111-121.
O. Duman and M. Gürcan, Some characterizations on statistical convergence of expected values of random variables, J. Math. Anal. 1 (2010) 1-8.
G. A. Anastassiou and O. Duman, Uniform approximation in statistical sense by double Gauss-Weierstrass singular integral operators, Nonlinear Funct. Anal. Appl. 15 (2010) 487-502.
V. Gupta and O. Duman, Bernstein-Durrmeyer type operators preserving linear functions, Mat. Vesnik 62 (2010) 259-264.
G. A. Anastassiou and O. Duman, Fractional trigonometric Korovkin theory in statistical sense, Serdica Math. J. 36 (2010) 121-136.
M. Bohner and O. Duman, Opial-type inequalities for diamond-alpha derivatives and integrals on time scales, Differ. Equ. Dyn. Syst. 18 (2010) 229-237.
G. A. Anastassiou and O. Duman, Statistical approximation by double Picard singular integral operators, Studia Univ. Babes-Bolyai Math. 55 (2010), 3-20.
M. Burgin and O. Duman, Fuzzy approximate continuity, J. Intell. Fuzzy Systems 20 (2009) 225-233.
O. Duman, Strong versions of the theorems of Weierstrass, Montel and Hurwitz, Hacettepe J. Math. Stat. 38 (2009) 153-159.
F. Dirik, O. Duman and K. Demirci, Statistical approximation to Bögel-type continuous and periodic functions, Cent. Eur. J. Math. 7 (2009) 539-549.
O. Duman and H. Merdan, Stability analysis of continuous population model involving predation and Allee effect, Chaos Solitons Fractals 41 (2009) 1218-1222.
M. A. Özarslan and O. Duman, Approximation theorems by Meyer-König and Zeller type operators, Chaos Solitons Fractals 41 (2009) 451-456.
O. Duman, M. A. Özarslan and B. Della Vecchia, Modified Szasz-Mirakjan-Kantorovich operators preserving linear functions, Turkish J. Math. 33 (2009) 151-158.
C. Çelik and O. Duman, Allee effect in a discrete-time predator-prey system, Chaos Solitons Fractals 40 (2009) 1956-1962.
H. Merdan and O. Duman, On the stability analysis of a general discrete-time population model involving predation and Allee effects, Chaos Solitons Fractals 40 (2009) 1169-1175.
G. A. Anastassiou and O. Duman, High order statistical fuzzy Korovkin theory, Stoch. Anal. Appl. 27 (2009) 543-554
H. Merdan, O. Duman, Ö. Akın and C. Çelik, Allee effects on population dynamics in continuous (overlapping) case, Chaos Solitons Fractals 39 (2009) 1994-2001.
G. A. Anastassiou, O. Duman and E. Erkuş-Duman, Statistical approximation for stochastic processes, Stoch. Anal. Appl. 27 (2009) 460-474.
G. A. Anastassiou and O. Duman, Statistical weighted approximation to derivatives of functions by linear operator, J. Comput. Anal. Appl. 11 (2009) 20-30.
Ö. Ocalan and O. Duman, Oscillation analysis of neutral difference equations with delays, Chaos Solitons Fractals 39 (2009) 261-270.
G. A. Anastassiou and O. Duman, On relaxing the positivity condition of linear operators in statistical Korovkin-type approximations, J. Comput. Anal. Appl. 11 (2009) 7-19
G. A. Anastassiou and O. Duman, Fractional Korovkin theory based on statistical convergence, Serdica Mathematical Journal 35 (2009) 381-396
M. A. Özarslan and O. Duman, A new approach in obtaining a better estimation in approximation by positive linear operators, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 58 (2009) 17-22.
G. A. Anastassiou and O. Duman, Statistical approximation to periodic functions by a general class of linear operators, J. Concr. Appl. Math. 7 (2009) 200-207.
M. Burgin and O. Duman, Properties of fuzzy statistical limits, J. Intell. Fuzzy Systems 19 (2008) 385-392.
M. A. Özarslan and O. Duman, Approximation properties of Poisson integrals for orthogonal expansions, Taiwanese J. Math. 12 (2008) 1147-1163.
M. A. Özarslan, O. Duman and H. M. Srivastava, Statistical approximation results for Kantorovich-type operators involving some special functions, Math. Comput. Modelling 48 (2008) 388-401.
O. Duman, A-Statistical convergence of sequences of convolution operators, Taiwanese J. Math. 12 (2008) 523-536.
M. Burgin and O. Duman, Statistical fuzzy convergence, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 16 (2008) 879-902.
O. Duman and C. Orhan, Rates of A-statistical convergence of operators in the space of locally integrable functions, Appl. Math. Lett. 21 (2008) 431-435.
C. Çelik, H. Merdan, O. Duman and Ö. Akın, Allee effects on population dynamics with delay, Chaos Solitons Fractals 37 (2008) 65-74.
E. Erkuş-Duman and O. Duman, Integral-type generalizations of operators obtained from certain multivariate polynomials, Calcolo 45 (2008) 53-67.
M. A. Özarslan and O. Duman, Local approximation results for Szasz-Mirakjan type operators, Arch. Math. (Basel) 90 (2008) 144-149.
O. Duman and G. A. Anastassiou, On statistical fuzzy trigonometric Korovkin theory, J. Comput. Anal. Appl. 10 (2008) 333-344.
G. A. Anastassiou and O. Duman, A Baskakov type generalization of statistical Korovkin theory, J. Math. Anal. Appl. 340 (2008) 476-486.
O. Duman, M. A. Özarslan and H. Aktuğlu, Better error estimation for Szasz-Mirakjan-Beta operators, J. Comput. Anal. Appl. 10 (2008) 53-59.
S. Karakuş, K. Demirci and O. Duman, Equi-statistical convergence of positive linear operators, J. Math. Anal. Appl. 339 (2008) 1065-1072.
G. A. Anastassiou and O. Duman, Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl. 55 (2008) 573-580.
S. Karakus, K. Demirci and O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Solitons Fractals 35 (2008) 763-769.
O. Duman and M.A. Özarslan, Szasz-Mirakjan type operators providing a better error estimation, Appl. Math. Lett. 20 (2007) 1184-1188.
B. Della Vecchia and O. Duman, Weighted approximation by Meyer-König and Zeller type operators, Studia Sci. Math. Hungar. 44 (2007) 445-467.
M. A. Özarslan and O. Duman, MKZ type operators providing a better estimation on [1/2,1), Canadian Math. Bull. 50 (2007) 434-439.
O. Duman, Regular matrix transformations and rates of convergence of positive linear operators, Calcolo 44 (2007) 159-165.
O. Duman, Korovkin type approximation theorems via I-convergence, Czechoslovak Math. J. 57 (2007) 367-375.
O. Duman, Higher order generalization of positive linear operators defined by a class of Borel measures, Turkish J. Math. 31 (2007) 333-339.
O. Duman and E. Erkuş, Approximation of continuous periodic functions via statistical convergence, Comput. Math. Appl. 52 (2006) 967-974.
E. Erkuş, O. Duman and H. M. Srivastava, Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials, Appl. Math. Comput. 182 (2006) 213-222.
O. Duman, E. Erkuş and V. Gupta, Statistical rates on the multivariate approximation theory, Math. Comput. Modelling 44 (2006) 763-770.
O. Duman, Statistical approximation theorems by k-positive linear operators, Arch. Math. (Basel) 86 (2006) 569-576.
O. Duman, M. A. Özarslan and O. Doğru, On integral type generalizations of positive linear operators, Studia Math. 174 (2006) 1-12.
O. Doğru and O. Duman, Statistical approximation of Meyer König and Zeller operators based on q-integers, Publ. Math. Debrecen 68 (2006) 199-214.
E. Erkuş and O. Duman, A Korovkin type approximation theorem in statistical sense, Studia Sci. Math. Hungar. 43 (2006) 285-294.
O. Duman and C. Orhan, An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen 69 (2006) 33-46.
M. A. Özarslan, O. Duman and O. Doğru, A-Statistical convergence for a class of positive linear operators, Rev. Anal. Numér. Théor. Approx. 35 (2006) 161-172.
E. Erkuş and O. Duman, A-statistical extension of the Korovkin type approximation theorem, Proc. Indian Acad. Sci. Math. Sci. 115 (2005) 499-508.
M. A. Özarslan, O. Duman and O. Doğru, Rates of A-statistical convergence of approximating operators, Calcolo 42 (2005) 93-104.
O. Duman and C. Orhan, Rates of A-statistical convergence of positive linear operators, Appl. Math. Lett. 18 (2005) 1339-1344.
O. Duman, The effects of matrix summability methods on bounds of function sequences, Appl. Math. Lett. 17 (2004) 1221-1229.
O. Duman and C. Orhan, Statistical approximation by positive linear operators, Studia Math. 161 (2004) 187-197.
O. Duman and C. Orhan, Mu-Statistically convergent function sequences, Czechoslovak Math. J. 54 (2004) 413-422.
O. Duman and C. Orhan, Statistical approximation in the space of locally integrable function, Publ. Math. Debrecen 63 (2003) 133-144.
O. Duman, M. K. Khan and C. Orhan, A-statistical convergence of approximatig operators, Math. Inequal. Appl. 6 (2003) 689-699.
O. Doğru, O. Duman and C. Orhan, Statistical approximation by generalized Meyer-König and Zeller type operators, Studia Sci. Math. Hungar. 40 (2003) 359-371.
O. Duman, Statistical approximation for periodic functions, Demonstratio Math. 36 (2003) 873-878.