Szász-integral operators linking general-Appell polynomials and approximation

Nadeem Rao; Mohammad Farid; Nand Kishor Jha; Nadeem Rao; Mohammad Farid; Nand Kishor Jha

doi:10.3934/math.2025623

AIMS Mathematics

2025, Volume 10, Issue 6: 13836-13854. doi: 10.3934/math.2025623

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Szász-integral operators linking general-Appell polynomials and approximation

1.
Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali-140413, Punjab, India
2.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
3.
Department of Mathematics, Chandigarh University, Mohali-140413, Punjab, India

Received: 31 January 2025 Revised: 22 May 2025 Accepted: 28 May 2025 Published: 16 June 2025
MSC : 41A25, 41A30, 41A35, 41A36

This manuscript is associated with a study of general Appell polynomials. In this research work, we introduced a new sequence of Szász-Integral type of sequence of operators via general-Appell polynomials to discuss approximation properties for Lebesgue integrable functions $ (L^p[0, \infty)) $. In addition, estimates are studied in view of test functions and central moments. Next, the convergence rate is discussed using the Korovkin theorem and a Voronovskaja-type theorem. Moreover, direct approximation results via modulus of continuity of first and second order, Peetre's K-functional, Lipschitz type space, and the $ r^{th} $ order Lipschitz type maximal functions are investigated. In the following section, we present weighted approximation results, and statistical approximation theorems are discussed.
- modulus of smoothness,
- mathematical operators,
- Szász operator,
- Appell polynomials,
- approximation algorithms,
- order of approximation,
- rate of convergence
Citation: Nadeem Rao, Mohammad Farid, Nand Kishor Jha. Szász-integral operators linking general-Appell polynomials and approximation[J]. AIMS Mathematics, 2025, 10(6): 13836-13854. doi: 10.3934/math.2025623

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Abstract

This manuscript is associated with a study of general Appell polynomials. In this research work, we introduced a new sequence of Szász-Integral type of sequence of operators via general-Appell polynomials to discuss approximation properties for Lebesgue integrable functions $ (L^p[0, \infty)) $. In addition, estimates are studied in view of test functions and central moments. Next, the convergence rate is discussed using the Korovkin theorem and a Voronovskaja-type theorem. Moreover, direct approximation results via modulus of continuity of first and second order, Peetre's K-functional, Lipschitz type space, and the $ r^{th} $ order Lipschitz type maximal functions are investigated. In the following section, we present weighted approximation results, and statistical approximation theorems are discussed.

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