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# On shape parameter $\alpha$ based approximation properties and $q$-statistical convergence of Baskakov-Gamma operators

Version 1 : Received: 24 January 2022 / Approved: 25 January 2022 / Online: 25 January 2022 (13:34:35 CET)

How to cite: Chen, M.; Nasiruzzaman, M.; Ayman Mursaleen, M.; Rao, N. On shape parameter $\alpha$ based approximation properties and $q$-statistical convergence of Baskakov-Gamma operators. Preprints 2022, 2022010383 (doi: 10.20944/preprints202201.0383.v1). Chen, M.; Nasiruzzaman, M.; Ayman Mursaleen, M.; Rao, N. On shape parameter $\alpha$ based approximation properties and $q$-statistical convergence of Baskakov-Gamma operators. Preprints 2022, 2022010383 (doi: 10.20944/preprints202201.0383.v1).

## Abstract

We construct a novel family of summation-integral type hybrid operators in terms of shape parameter $\alpha\in \lbrack 0,1]$ in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre's K-functional, Lipschitz class, and second-order modulus of smoothness.

## Keywords

Baskakov operators; gamma operators; rate of convergence; Lipschitz maximal space; q-density; q-statistical convergence.

## Subject

MATHEMATICS & COMPUTER SCIENCE, General Mathematics

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