Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(2): 359-373

Online first article March 9, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b140625

Copyright © The Korean Mathematical Society.

Stancu type generalization of modified Gamma operators based on $q$-integers

Shu-Ni Chen, Wen-Tao Cheng, and Xiao-Ming Zeng

Xiamen University, Anqing Normal University, Xiamen University

Abstract

In this paper, we propose the Stancu type generalization of a kind of modified $q$-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.

Keywords: modified $q$-Gamma-Stancu operators, approximation theorem, weighted approximation, rate of convergence

MSC numbers: 41A10, 41A25, 41A36