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Mathematica Slovaca

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Volume 68, Issue 4

Issues

Approximation by Baskakov-Durrmeyer operators based on (p, q)-integers

Tuncer Acar / Ali Aral / Mohammad Mursaleen
Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0153

Abstract

In the present paper, we introduce a new sequence of linear positive operators based on (p, q)-integers. To approximate functions over unbounded intervals, we introduce Baskakov-Durrmeyer type operators using the (p, q)-Gamma function. We investigate rate of convergence of new operators in terms of modulus of continuities and obtain their approximation behavior for the functions belonging to Lipschitz class. At the end, we present a modification of new operators preserving the test function x.

MSC 2010: Primary 41A35; Secondary 41A25

Keywords: (p, q)-integers; (p, q)-Gamma function; (p, q)-Baskakov-Durrmeyer operators; rate of convergence

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About the article

Received: 2016-09-26

Accepted: 2017-03-08

Published Online: 2018-08-06

Published in Print: 2018-08-28


Communicated by Gregor Dolinar


Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 897–906, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0153.

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