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Journal of Applied Mathematics and Computing

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28-01-2016 | Original Research

On (p, q)-analogue of modified Bernstein–Schurer operators for functions of one and two variables

Author: Qing-Bo Cai

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

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Abstract

In this paper, we introduce a new kind of modified Bernstein–Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Next, we construct the bivariate operators and get some convergence properties. Finally, we give some graphs to illustrate the convergence properties of operators to some functions.

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Title: On (p, q)-analogue of modified Bernstein–Schurer operators for functions of one and two variables
Author: Qing-Bo Cai
Publication date: 28-01-2016
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-016-0991-1

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