Convergence of derivative of Szász type operators involving Charlier polynomials

Purshottam N. Agrawal; Thakur Ashok K. Sinha; Avinash Sharma

doi:10.3934/mfc.2021016

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2022, Volume 5, Issue 1: 1-15. Doi: 10.3934/mfc.2021016

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Convergence of derivative of Szász type operators involving Charlier polynomials

1.
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India
2.
Post Graduate Department of Mathematics, Patliputra University, Patna 800020, India
3.
Post Graduate Department of Mathematics, Magadh University, Bodh Gaya, Gaya 824234, India

Received: April 30, 2021

Revised: June 30, 2021

Early access: September 2021

Published: February 2022

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Abstract

The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [20]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the $ (2k+2)th $ order modulus of continuity using Steklov mean.

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Mathematics Subject Classification: 41A36, 41A25, 41A28, 26A15.

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