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Bull. Korean Math. Soc. 2013; 50(4): 1145-1156
Printed July 1, 2013
https://doi.org/10.4134/BKMS.2013.50.4.1145
Copyright © The Korean Mathematical Society.
On statistical approximation properties of modified $q$-Bernstein-Schurer Operators
Mei-Ying Ren and Xiao-Ming Zeng
Wuyi University, Xiamen University
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
MSC numbers: Primary 41A10, 41A25; Secondary 41A36
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