Degree of approximation for bivariate extension of blending type \(q\)-Durrmeyer operators based on Pólya distribution

Volume 24, Issue 3, pp 256--272 http://dx.doi.org/10.22436/jmcs.024.03.07

Publication Date: March 06, 2021 Submission Date: February 01, 2021 Revision Date: February 17, 2021 Accteptance Date: February 19, 2021

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Authors

Edmond Aliaga - Department of Mathematics, University of Prishtina, Prishtina, Kosovo. Shpetim Rexhepi - Mother Teresa University, Skopje, North Macedonia.

Abstract

In this paper we introduce a bivariate of \(q\)-Durrmeyer variant of generalized Bernstein operators by using Pólya distribution. The convergence rate of these operators is examined by means of the Lipschitz class and the modulus of continuity. Furthermore, we obtain a Voronovskaja type symptotic formula, error estimation in terms of the partial modulus of continuity and Peetre's K-functional.

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Keywords

• Durrmeyer operators
• K-functional
• modulus of continuity
• Pólya distribution

MSC

•  41A36
•  40C15
•  40G10
•  46E30

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