On approximation process by certain modified Dunkl generalization of Szász-Beta type operators

Volume 19, Issue 1, pp 9--18 http://dx.doi.org/10.22436/jmcs.019.01.02

Publication Date: February 21, 2019 Submission Date: July 23, 2018 Revision Date: November 23, 2018 Accteptance Date: December 20, 2018

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Authors

Çiğdem Atakut - Department of Mathematics, Faculty of Science, Ankara University, Ankara, Turkey. Seda Karateke - Department of Mathematics and Computer Science, Faculty of Science and Letters, Istanbul Arel University, Istanbul, Turkey. Ibrahim Büyükyazıcı - Department of Mathematics, Faculty of Science, Ankara University, Ankara, Turkey.

Abstract

In this paper, we give a generalization of the Szász-Beta type operators generated by Dunkl generalization of exponential function and obtain convergence properties of these operators by using Korovkin's theorem and weighted Korovkin-type theorem. We also establish the order of convergence by using the modulus of smoothness and the weighted modulus of continuity.

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Keywords

• Dunkl type generalization
• Genuine Szász beta operators
• modulus of smoothness
• Lipschitz functions

MSC

•  41A10
•  41A25
•  41A36

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