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Research Article | Open Access

Approximation properties of Stancu type Szász-Mirakjan operators

Bo-Yong Lian1( ), Qing-Bo Cai2
Department of Mathematics, Yang-en University, Quanzhou 362000, China
School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
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Abstract

In this paper, a class of Stancu type Szász-Mirakjan operators are introduced. The approximation properties of the operators are discussed using tools of modulus of continuity, modulus of smoothness and K-functional. The estimation of the Lipschitz function class by the operators is also studied. Later, the Voronvskaya type asymptotic expansion of the operators is established. Finally, we compare the convergence of these newly defined operators for certain functions with certain graphs.

Keywords

Szász-Mirakjan operatorsmodulus of continuityK-functionalVoronovskaya-type asymptotic formularate of convergence
CLC number: 41A10, 41A25, 41A36

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 21769-21780
DOI: 10.3934/math.20231110

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Cite this article:
Lian B-Y, Cai Q-B. Approximation properties of Stancu type Szász-Mirakjan operators. AIMS Mathematics, 2023, 8(9): 21769-21780. https://doi.org/10.3934/math.20231110

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Received: 16 May 2023
Revised: 25 June 2023
Accepted: 29 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)