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March 2022 On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter $\lambda$
Resat Aslan
Adv. Studies: Euro-Tbilisi Math. J. 15(1): 151-166 (March 2022). DOI: 10.32513/asetmj/19322008210

Abstract

This paper deals with some approximation properties of Stancu-Kantorovich variant of Sz\'{a}sz-Mirakjan operators based on B\'{e}zier basis functions with shape parameter $\lambda\in\lbrack-1,1]$. We compute several preliminary results such as moments and central moments. Later, we introduce a Korovkin-type convergence theorem and discuss the order of approximation in terms of the modulus of continuity and for the elements belong to Lipschitz-type class and Peetre's $K$-functional, respectively. Also, we prove a Voronovskaya type asymptotic theorem. Lastly, we present the comparison of the convergence of constructed operators to the certain functions with some graphical illustrations for different values of $m$, $\alpha$, $\beta$ and $\lambda$ parameters.

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The current pdf replaces the original pdf file, first available on 5 April 2022. The new version corrects the DOI prefix to read 10.32513.

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Resat Aslan. "On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter $\lambda$." Adv. Studies: Euro-Tbilisi Math. J. 15 (1) 151 - 166, March 2022. https://doi.org/10.32513/asetmj/19322008210

Information

Received: 23 September 2021; Accepted: 10 December 2021; Published: March 2022
First available in Project Euclid: 5 April 2022

Digital Object Identifier: 10.32513/asetmj/19322008210

Subjects:
Primary: 41A10
Secondary: 41A25 , 41A36

Keywords: Lipschitz-type class , modulus of continuity , order of approximation , shape parameter $\lambda$ , Voronovskaya type asymptotic theorem

Rights: Copyright © 2022 Tbilisi Centre for Mathematical Sciences

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Vol.15 • No. 1 • March 2022
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