Browse > Article
http://dx.doi.org/10.4134/BKMS.2013.50.4.1145

ON STATISTICAL APPROXIMATION PROPERTIES OF MODIFIED q-BERNSTEIN-SCHURER OPERATORS  

Ren, Mei-Ying (Department of Mathematics and Computer Science Wuyi University)
Zeng, Xiao-Ming (Department of Mathematics Xiamen University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 1145-1156 More about this Journal
Abstract
In this paper, a kind of modified $q$-Bernstein-Schurer operators is introduced. The Korovkin type statistical approximation property of these operators is investigated. Then the rates of statistical convergence of these operators are also studied by means of modulus of continuity and the help of functions of the Lipschitz class. Furthermore, a Voronovskaja type result for these operators is given.
Keywords
modified q-Bernstein-Schurer operators; statistical approximation property; modulus of continuity; rate of statistical convergence; Voronovskaja type result;
Citations & Related Records
연도 인용수 순위
  • Reference
1 O. Dalmanoglu and O. Dogru, On statistical approximation properties of Kantorovich type q-Bernstein operators, Math. Comput. Modelling 52 (2010), no. 5-6, 760-771.   DOI   ScienceOn
2 O. Dogru and K. Kanat, On statistical approximation properties of the Kantorovich type Lupas operators, Math. Comput. Modelling 55 (2012), no. 3-4, 1610-1621.   DOI   ScienceOn
3 O. Dogru, On statistical approximation properties of Stancu type bivariate generalization of q-Balas-Szabados operators in: Numerical analysis and approximation theory, 179-194, Casa Cartii de stiinta, Cluj-Napoca, 2006.
4 S. Ersan and O. Dogru, Statistical approximation properties of q-Bleimann, Butzer and Hahn operators, Math. Comput. Modelling 49 (2009), no. 7-8, 1595-1606.   DOI   ScienceOn
5 H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.   DOI
6 V. Gupta and C. Radu, Statistical approximation properties of q-Baskokov-Kantorovich operators, Cent. Eur. J. Math. 7 (2009), no. 4, 809-818.   DOI
7 G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its applications, Cambridge University press, Cambridge, UK, Vol. 35, 1990.
8 A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), no. 1, 129-138.   DOI   ScienceOn
9 V. G. Kac and P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, New York, 2002.
10 C. V. Muraru, Note on q-Bernstein-Schurer operators, Stud. Univ. Babes-Bolyai Math. 56 (2011), no. 2, 480-495.
11 I. Niven, H. S. Zuckerman, and H. Montgomery, An Introduction to the Theory Numbers, 5th ed. Wiley, New York, 1991.
12 M. Orkcu and O. Dogru, Weighted statistical approximation by Kantorovich type q-Szasz-Mirakjan operators, Appl. Math. Comput. 217 (2011), no. 20, 7913-7919.   DOI   ScienceOn
13 G. M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997), no. 1-4, 511-518.
14 F. Schurer, Linear positive operators in approximation theory, Math. Inst. Techn. Univ. Delft: Report, 1962.