OKTAY DUMAN OKTAY DUMAN. Full Professor of Math. Date of Birth: July 23, 1975

Transcription

1 OKTAY DUMAN TOBB Economics and Technology University OKTAY DUMAN Full Professor of Math. Date of Birth: July 23, 1975 TOBB Economics and Technology University Department of Mathematics Söğütözü TR-06530, Ankara, Turkey Website: Education Ph.D. : Ankara University ( ) M.S. : Ankara University ( ) B.S. : Ankara University ( ) [Adresinizi yazın] [Telefon numaranızı yazın] [E-posta adresinizi yazın] Academic Degrees Full Professor : TOBB ETU (2010- ) Associate Professor : TOBB ETU ( ) Assistant Professor : TOBB ETU ( ) Research Assistant : Ankara University ( ) Reserach Areas Statistical convergence and its applications (40A35; 40G15) Korovkin-type approximation theory (41A35; 41A36) Rates of convergence (41A25) Approximation in the complex domain (30E10) Awards and Honors Associate Member of TUBA (The Turkish Academy of Sciences [ ] Research Reward Dedicated to "Professor M. Gündüz İkeda" [Math. Foundation, METU, Ankara, 2005]

2 Editorial Reviewer : AMS-Mathematical Reviews Editorial Board : Journal of Computational Analysis and Applications Journal of Concrete and Applicable Mathematics Journal of Applied Functional Analysis Journal of Mathematical Analysis Professional Memberships The Mathematical Association of America - MAA ( ) American Mathematical Society - AMS ( ) Refereeing J. Approx. Theory (SCI) J. Comput. Appl. Math. (SCI) Appl. Math. Lett. (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. Math. Slovaca Math. Comput. Modelling Rocky Mountain J. Math. Studia Sci. Math. Hungar. Positivity Miskolc Math. Notes Information Sciences Appl. Math. Comput J. Inequal. Appl. Abst. Appl. Anal. Math. Model. Anal. Turkish J. Math. Iran. J. Fuzzy Syst. Hacettepe J. Math. Stat. Math. Commun. Discrete Dynam Nat. Soc. J. Appl. Math. Indian J. Pure and Appl. Math. Acta Math. Appl. Sinica (AMS-MR) Internat. J. Math. Math. Sci. (AMS-MR) Comput. Lett. (AMS-MR) 2

3 J. Math. Control Sci. Appl. (AMS-MR) Kyungpook Math. J. (AMS-MR) Assian Bull. Math. (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) Projects O. Duman, Statistical approximation of linear operators by means of summability theory, Principle Investigator, TUBITAK 1002 Project, No: 108T229, 15 May May C. Orhan, E. Bayram, O. Duman and M. Adıvar, Statistically Convergent Function Sequences, Investigator, TUBITAK BAYG Project, 15 September September Graduate Students Ceylan Turan (TOBB ETU, Ph.D., ) İsmail Aslan (TOBB ETU, M.S., ) Nisa Küçük (TOBB ETU, M.S., ) Engin Sarı (TOBB ETU, M.S., ) Ceylan Turan (TOBB ETU, M.S., 2012) Alperen Ali Ergür (TOBB ETU, M.S., 2011) Merve Kester (TOBB ETU, M.S., 2011) Administirative Duties in the University Vice Dean of Faculty of Arts and Sciences in TOBB ETU (2013- ) Member of Administirative Board of Faculty of Arts and Sciences in TOBB ETU (2012- ) Member of Administirative Board of Faculty of Arts and Sciences in TOBB ETU ( ) Vice President of the Dept. of Math. in TOBB ETU ( ) Administirative Duties in Conferences Co-Chair of Minisymposium: Approximation Theory and Special Functions in the 11th International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2013, Rhodes, Greece, September,

4 Member of Scientific Committee: 8th Ankara Mathematics Days, Hacettepe Üniversity, June 13-14, Member of Scientific Committee: 7th Ankara Mathematics Days, Bilkent Üniversity, May 31 June 01, Conference Chair: International Conference on Applied Mathematics and Approximation Theory AMAT 2012, TOBB ETU, Ankara- Turkey, May 17-20, Conference Chair: 5th Ankara Mathematics Days, TOBB ETU, Ankara-Turkey, June 03-04, Member of Scientific Committee: International Workshop on New Trends in Science and Technology, Çankaya University, Ankara- Turkey, November 03-04, Member of Organizing Committee: 1. Üstün Yetenekli Çocuklar Kongresi, İstanbul-Turkey, September 23-25, Courses Taught Approximation Theory (graduate) Functions Theory (graduate) Real Analysis I (graduate) Real Analysis II (graduate) 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, Toplanabilme teorisinin yaklaşımlar teorisi üzerindeki etkileri, Anadolu Üniversitesi, Matematik Bölümü, Eskişehir-Türkiye, 23 Mayıs O. Duman, Yaklaşımlar teorisinde yeni yaklaşım tekniklerinin ihtiyacı, TÜBA Konferansı, Karabük Üniversitesi, Matematik Bölümü, Karabük-Türkiye, 26 Nisan O. Duman, Convergence methods in approximation theory, Bilkent University, Department of Mathematics, Ankara-Turkey, November 16, O. Duman, Recent developments in approximation theory, TOBB Economics and Technology University, Department of Mathematics, Ankara -Turkey, October 12, O. Duman, Recent improvements on statistical approximation theory, Izmir University of Economics, Department of Mathematics, İzmir- Turkey, April 26,

5 O. Duman, Uniform statistical approximation by double Gauss- Weierstrass singular integral operators, Gazi University, Department of Mathematics, Ankara-Turkey, November 06, O. Duman, A Baskakov type generalization of statistical Korovkin theory, Ankara University, Department of Mathematics, Ankara- Turkey, April 15, 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, O. Duman, On relaxing the positivity condition of linear operators in statistical Korovkin-type approximations, Ankara University, Department of Mathematics, Ankara-Turkey, April 30, O. Duman, Allee effects on population Dynamics, Çankaya University, Nano-Science and Research Center, Ankara-Turkey, December 27, O. Duman, Approximation properties of positive linear operators, Çankaya University, Department of Mathematics and Computer Science, Ankara-Turkey, December 15, 2006 O. Duman, Statistical approximation by positive linear operators, Middle East Technical University, Department of Mathematics, Ankara-Turkey, March 24, O. Duman, A-statistical convergence of approximating operators, Ankara University, Department of Mathematics, Ankara-Turkey, May 20, International/National Contributed Talks 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, O. Duman, Summability process by Mastoianni operators, 26 th National Mathematics Symposium, Diyarbakır-Turkey, September 4-7, C. Turan and O. Duman, Statistical convergence on time scales, International Conference on Applied Mathematics and Approximation Theory AMAT 2012, TOBB ETU, Ankara-Turkey, May 17-20, 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, G.A. Anastassiou and O. Duman, Statistical approximation by double Picard singular integral operators, 4th Ankara Mahematics Days, METU, Ankara-Turkey, June 04-05,

6 O. Duman, Stability analysis of population dynamics under Allee effects (poster presentation), International Workshop on New Trends in Science and Technology, Çankaya University, Ankara-Turkey, November 03-04, 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, 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-Turkey, May 22-23, 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-Turkey, July 04-07, O. Duman, Stability analysis of delay population dynamics under Allee effects (poster presentation), TASSA Conference, Yale University, New Haven-USA, March 24-25, O. Duman and M.A. Özarslan, MKZ type positive linear operators providing a better error estimation, 19th National Mathematics Symposium, Kütahya-Turkey, August 22-25, O. Duman and C. Orhan, Rates of A-statistical convergence of positive linear operators, Fejer-Riesz Conference, Eger-Hungary, June 09-13, Citation Report (ISI Web of Science) Sum of the papers published: 78 Sum of the times cited: 617 Sum of the times cited without self citations: 412 Citing articles: 251 Citing articles without self-citations: 188 Average citations per item: 7.91 h-index: 14 PUBLICATIONS A. Books: 1. [EDITED-BOOK] G.A. Anastassiou and O. Duman (eds.), Advaces in Applied Mathematics and Approximation Theory, Springer Proceedings in Mathematics & Statistics, Vol. 41, Springer, New York, 2013 (486 p.) 6

7 2. [MONOGRAPH-BOOK] G.A. Anastassiou and O. Duman, Towards Intelligent Modeling: Statistical Approximation Theory, Intelligent Systems Reference Library, Vol. 14, Springer, Berlin, 2011 (234 p.) B. Articles: 1. O. Duman, Nonlinear Bernstein-type operators providing better error estimation, Miskolc. Math. Notes (accepted for publication). 2. O. Duman, Summability process by Mastroianni operators and their generalizations, Mediterr. J. Math. (accepted for publication). 3. O. Duman, Summability process by singular operators, Publ. Math. Debrecen (accepted for publication). 4. C. Turan and O. Duman, Convergence methods on time scales, AIP Conf. Proc (2013) C. Turan and O. Duman, Statistical convergence on time scales and its characterizations, Advances in Applied Mathematics and Approximation Theory, Springer Proc. Math. Stat. 41 (2013) (AMS-MR) 6. A.A. Ergür and O. Duman, Generalization of statistical Korovkin theorems, J. Appl. Math. 2013, Article ID , 5p. (SCI- 7. 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) O. Duman and M. Kester, Statistical approximation by double Poisson-Cauchy singular integral operators, Results Math. 62 (2012) A.D. Gadjiev, O. Duman and A.M. Ghorbanalizadeh, Ideal convergence of k-positive linear operators, J. Funct. Spaces Appl. 2012, Article ID , 12 p. 10. O. Duman and E. Erkuş-Duman, Statistical Korovkin-type theory for matrix-valued functions, Studia Sci. Math. Hungarica 48 (2011) H. Aktuğlu, M.A. Özarslan and O. Duman, Matrix summability methods on the approximation of multivariate q-mkz operators, Bull. Malaysian Math. Sci. Soc. (2); 34 (2011) (SCI- 12. G.A. Anastassiou and O. Duman, Statistical approximation by double complex Gauss-Weierstrass integral operators, Appl. Math. Lett. 24 (2011) M.A. Özarslan, O. Duman and N.I. Mahmudov, Local approximation properties of modified Baskakov operators, Results Math. 59 (2011) A. Aral and O. Duman, A Voronovskaya-type formula for SMK operators via statistical convergence, Math. Slovaca 61 (2011)

8 15. G.A. Anastassiou and O. Duman, Statistical Lp-convergence of double smooth Picard singular integral operators, J. Comput. Anal. Appl. 13 (2011) M. Burgin and O. Duman, Approximation by linear operators in spaces of fuzzy continuous functions, Positivity 15 (2011) O. Duman and M.A. Özarslan, Global approximation results for modified Szasz-Mirakjan operators, Taiwanese J. Math. 15 (2011) (SCI) 18. 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) M. Burgin and O. Duman, Approximate fuzzy continuity of fuznctions, Internat. J. Fuzzy Syst. Appl. 1 (2011) O. Duman, Statistical fuzzy approximation to fuzzy differentiable functions by fuzzy linear operators, Hacettepe J. Math. Stat. 39 (2010) M.A. Özarslan and O. Duman, Local approximation behavior of modified SMK operators, Miskolc Math. Notes 11 (2010) O. Duman, Statistical convergence of max-product approximating operators, Turkish J. Math. 34 (2010) F. Dirik, O. Duman and K. Demirci, Approximation in statistical sense to B-continuous functions by positive linear operators, Studia Sci. Math. Hungarica 47 (2010) M.A. Özarslan and O. Duman, Global approximation properties of modified SMK operators, Filomat 24 (2010) S. Karakuş, K. Demirci and O. Duman, Statistical approximation by positive linear operators on modular spaces, Positivity 14 (2010) G.A. Anastassiou and O. Duman, Statistical convergence of double complex Picard integral operators, Appl. Math. Lett. 23 (2010) (SCI) 27. 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) (SCI- 28. G.A. Anastassiou and O. Duman, Statistical Korovkin theory for multivariate stochastic processes, Stochastic Anal. Appl. 28 (2010) O. Duman, Fuzzy approximation based on statistical rates, Publ. Math. Debrecen 76 (2010) G.A. Anastassiou and O. Duman, Statistical Lp approximation by double Gauss-Weierstrass singular integral operators, Comput. Math. Appl. 59 (2010) (SCI) 31. O. Duman, M.A. Özarslan and E. Erkuş-Duman, Rates of ideal convergence for approximation operators, Mediterr. J. Math. 7 (2010)

9 32. O. Duman and M. Gürcan, Some characterizations on statistical convergence of expected values of random variables, J. Math. Anal. 1 (2010) G.A. Anastassiou and O. Duman, Uniform approximation in statistical sense by double Gauss-Weierstrass singular integral operators, Nonlinear Funct. Anal. Appl. 15 (2010) (AMS- MR) 34. V. Gupta and O. Duman, Bernstein-Durrmeyer type operators preserving linear functions, Mat. Vesnik 62 (2010) (AMS- MR) 35. G.A. Anastassiou and O. Duman, Fractional trigonometric Korovkin theory in statistical sense, Serdica Math. J. 36 (2010) (AMS-MR) 36. M. Bohner and O. Duman, Opial-type inequalities for diamondalpha derivatives and integrals on time scales, Differential Equations Dynam. Systems 18 (2010) (AMS-MR) 37. G.A. Anastassiou and O. Duman, Statistical approximation by double Picard singular integral operators, Studia Univ. Babes-Bolyai Math. 55 (2010) (AMS-MR) 38. M. Burgin and O. Duman, Fuzzy approximate continuity, J. Intell. Fuzzy Syst. 20 (2009) O. Duman, Strong versions of the theorems of Weierstrass, Montel and Hurwitz, Hacettepe J. Math. Stat. 38 (2009), (SCI- 40. F. Dirik, O. Duman and K. Demirci, Statistical approximation to Bögel-type continuous and periodic functions, Cent. Eur. J. Math. 7 (2009), O. Duman and H. Merdan, Stability analysis of continuous population model involving predation and Allee effect, Chaos, Solitons & Fractals 41 (2009), (SCI) 42. M.A. Özarslan and O. Duman, Approximation theorems by Meyer- König and Zeller type operators, Chaos, Solitons & Fractals 41 (2009), (SCI) 43. O. Duman, M.A. Özarslan and B. Della Vecchia, Modified Szasz- Mirakjan-Kantorovich operators preserving linear functions, Turkish J. Math. 33 (2009), C. Çelik and O. Duman, Allee effect in a discrete-time predatorprey system, Chaos, Solitons & Fractals 40 (2009), (SCI) 45. H. Merdan and O. Duman, On the stability analysis f a general discrete-time population model involving predation and Allee effects, Chaos, Solitons & Fractals 40 (2009), (SCI) 46. G.A. Anastassiou and O. Duman, High order statistical fuzzy Korovkin theory, Stochastic Anal. Appl. 27 (2009), (SCI- 47. H. Merdan, O. Duman, Ö. Akın and C. Çelik, Allee effects on population dynamics in continuous (overlapping) case, Chaos, Solitons & Fractals 39 (2009), (SCI) 48. G.A. Anastassiou, O. Duman and E. Erkuş-Duman, Statistical approximation for stochastic processes, Stochastic Anal. Appl. 27 (2009),

10 49. G.A. Anastassiou and O. Duman, Statistical weighted approximation to derivatives of functions by linear operators, J. Comput. Anal. Appl. 11 (2009), Ö. Ocalan and O. Duman, Oscillation analysis of neutral difference equations with delays, Chaos, Solitons & Fractals 39 (2009), (SCI) 51. 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), (SCI- 52. G.A. Anastassiou and O. Duman, Fractional Korovkin theory based on statistical convergence, Serdica Math. J. 35 (2009) (AMS-MR) 53. 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. Ser. A1 Math. Stat. 58 (2009) (AMS-MR) 54. G.A. Anastassiou and O. Duman, Statistical approximation to periodic functions by a class of linear operators, J. Concr. Appl. Math. 7 (2009), (AMS-MR) 55. M. Burgin and O. Duman, Properties of fuzzy statistical limits, J. Intell. Fuzzy Syst. 19 (2008), M.A. Özarslan and O. Duman, Approximation properties of Poisson integrals for orthogonal expansions, Taiwanese J. Math. 12 (2008), (SCI) 57. 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), O. Duman, A-Statistical convergence of sequences of convolution operators, Taiwanese J. Math. 12 (2008), (SCI) 59. M. Burgin and O. Duman, Statistical fuzzy convergence, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 16 (2008), O. Duman and C. Orhan, Rates of A-statistical convergence of operators in the space of locally integrable functions, Appl. Math. Lett. 21 (2008), (SCI) 61. C. Çelik, H. Merdan, O. Duman and Ö. Akın, Allee effects on population dynamics with delay, Chaos, Solitons & Fractals 37 (2008), (SCI) 62. E. Erkuş-Duman and O. Duman, Integral-type generalizations of the operators constructed by means of certain multivariate polynomials, Calcolo 45 (2008), M.A. Özarslan and O. Duman, Local approximation results for Szasz-Mirakjan type operators, Arch. Math. (Basel) 90 (2008), O. Duman and G.A. Anastassiou, On statistical fuzzy trigonometric Korovkin theory, J. Comput. Anal. Appl. 10 (2008), (SCI- 10

11 65. G.A. Anastassiou and O. Duman, A Baskakov type generalization of statistical Korovkin theory, J. Math. Anal. Appl. 340 (2008), (SCI) 66. O. Duman, M.A. Özarslan and H. Aktuğlu, Better error estimation for Szasz-Mirakjan-Beta operators, J. Comput. Anal. Appl. 10 (2008), S. Karakuş, K. Demirci and O. Duman, Equi-statistical convergence of positive linear operators, J. Math. Anal. Appl. 339 (2008), (SCI) 68. G.A. Anastassiou and O. Duman, Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl. 55 (2008), (SCI) 69. S. Karakuş, K. Demirci and O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons & Fractals 35 (2008), (SCI) 70. O. Duman and M.A. Özarslan, Szasz-Mirakjan type operators providing a better error estimation, Appl. Math. Lett. 20 (2007), ). (SCI) 71. B. Della Vecchia and O. Duman, Weighted approximation by Meyer-König and Zeller type operators, Studia Sci. Math. Hungarica 44 (2007), M.A. Özarslan and O. Duman, MKZ type operators providing a better estimation on [1/2,1), Canadian Math. Bull. 50 (2007), O. Duman, Regular matrix transformations and rates of convergence of positive linear operators, Calcolo 44 (2007), O. Duman, Korovkin type approximation theorems via I- convergence, Czech. Math. J. 57 (2007), O. Duman, Higher order generalization of positive linear operators defined by a class of Borel measures, Turkish J. Math. 31 (2007), O. Duman and E. Erkuş, Approximation of continuous periodic functions via statistical convergence, Comput. Math. Appl. 52 (2006), (SCI) 77. 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), O. Duman, E. Erkuş and V. Gupta, Statistical rates on the multivariate approximation theory, Math. Comput. Modelling 44 (2006), O. Duman, Statistical approximation theorems by k-positive linear operators, Arch. Math. (Basel) 86 (2006), O. Duman, M.A. Özarslan and O. Doğru, On integral type generalizations of positive linear operators, Studia Math. 174 (2006), (SCI) 81. O. Doğru and O. Duman, Statistical approximation of Meyer König and Zeller operators based on q-integers, Publ. Math. Debrecen (2006),

12 82. E. Erkuş and O. Duman, A Korovkin type approximation theorem in statistical sense, Studia Sci. Math. Hungarica 43 (2006), O. Duman and C. Orhan, An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen 69 (2006), M.A. Özarslan, O. Duman and O. Doğru, A-Statistical convergence for a class of positive linear operators, Rev. Anal. Numer. Theor. Approx. 35 (2006), (AMS-MR) 85. E. Erkuş and O. Duman, A-statistical extension of the Korovkin type approximation theorem, Proc. Indian. Acad. Sci. (Math. Sci.) 115 (2005), M.A. Özarslan, O. Duman and O. Doğru, Rates of A-statistical convergence of approximating operators, Calcolo 42 (2005), O. Duman and C. Orhan, Rates of A-statistical convergence of positive linear operators, Appl. Math. Lett. 18 (2005), (SCI) 88. O. Duman, The effects of matrix summability methods on bounds of function sequences, Appl. Math. Lett. 17 (2004), (SCI) 89. O. Duman and C. Orhan, Statistical approximation by positive linear operators, Studia Math. 161 (2004), (SCI) 90. O. Duman and C. Orhan, Mu-Statistically convergent function sequences, Czech. Math. J. 54 (2004), O. Duman and C. Orhan, Statistical approximation in the space of locally integrable functions, Publ. Math. Debrecen 63 (2003), O. Duman, M.K. Khan and C. Orhan, A-statistical convergence of approximatig operators, Math. Ineq. Appl. 6 (2003), (SCI- 93. O. Doğru, O. Duman and C. Orhan, Statistical approximation by generalized Meyer-König and Zeller type operators, Studia Sci. Math. Hungarica 40 (2003), O. Duman, Statistical approximation for periodic functions, Demonstratio Math. 36 (2003), (AMS-MR) Last updated: June 27, 2014 go to the first page 12