Approximation by a new generalization of Szász-Mirakjan operators via \((p,q)\)-calculus

Volume 14, Issue 5, pp 310--323 http://dx.doi.org/10.22436/jnsa.014.05.02

Publication Date: January 23, 2021 Submission Date: December 10, 2020 Revision Date: December 22, 2020 Accteptance Date: December 27, 2020

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Authors

Reşat Aslan - Provincial Directorate of Labor and Employment Agency, 63050, Şanlıurfa, Turkey. Aydin Izgi - Department of Mathematics, Faculty of Sciences and Arts, Harran University, 63100, Şanlıurfa, Turkey.

Abstract

In this work, we obtain the approximation properties of a new generalization of Szász-Mirakjan operators based on post-quantum calculus. Firstly, for these operators, a recurrence formulation for the moments is obtained, and up to the fourth degree, the central moments are examined. Then, a local approximation result is attained. Furthermore, the degree of approximation in respect of the modulus of continuity on a finite closed set and the class of Lipschitz are computed. Next, the weighted uniform approximation on an unbounded interval is showed, and by the modulus of continuity, the order of convergence is estimated. Lastly, we proved the Voronovskaya type theorem and gave some illustrations to compare the related operators' convergence to a certain function.

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Keywords

• Weighted approximation
• Szász-Mirakjan operators
• modulus of continuity
• \((p,q)\)-calculus

MSC

•  41A25
•  41A35
•  41A36

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