Generalization of Szász operators involving multiple Sheffer polynomials

Mahvish Ali; Richard B. Paris

doi:10.1007/s41478-022-00443-9

Generalization of Szász operators involving multiple Sheffer polynomials

Mahvish Ali^*, Richard B. Paris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The present work deals with the mathematical investigation of some generalizations of the Szász operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Szász operators involving multiple Sheffer polynomials are considered. Convergence properties of these operators are verified with the help of the universal Korovkin-type result and the order of approximation is calculated by using classical modulus of continuity. Further, the convergence of these operators are also discussed in weighted spaces of functions on the positive semi-axis and estimate the approximation with the help of weighted modulus of continuity. The theoretical results are exemplified choosing the special cases of multiple Sheffer polynomials.

Original language	English
Number of pages	19
Journal	Journal of Analysis
Early online date	26 May 2022
DOIs	https://doi.org/10.1007/s41478-022-00443-9
Publication status	E-pub ahead of print - 26 May 2022

Keywords

Szász operators
Modulus of continuity
Rate of convergence
Multiple Sheffer polynomials

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title = "Generalization of Sz{\'a}sz operators involving multiple Sheffer polynomials",

abstract = "The present work deals with the mathematical investigation of some generalizations of the Sz{\'a}sz operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Sz{\'a}sz operators involving multiple Sheffer polynomials are considered. Convergence properties of these operators are verified with the help of the universal Korovkin-type result and the order of approximation is calculated by using classical modulus of continuity. Further, the convergence of these operators are also discussed in weighted spaces of functions on the positive semi-axis and estimate the approximation with the help of weighted modulus of continuity. The theoretical results are exemplified choosing the special cases of multiple Sheffer polynomials.",

author = "Mahvish Ali and Paris, {Richard B.}",

note = "Funding Information: This work has been sponsored by a Dr. D. S. Kothari Post Doctoral Fellowship (Award letter No. F.4-2/2006(BSR)/MA/17-18/0025) awarded to Dr. Mahvish Ali by the University Grants Commission, Government of India, New Delhi. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to The Forum D{\textquoteright}Analystes.",

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month = may,

day = "26",

doi = "10.1007/s41478-022-00443-9",

language = "English",

journal = "Journal of Analysis",

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AU - Ali, Mahvish

AU - Paris, Richard B.

N1 - Funding Information: This work has been sponsored by a Dr. D. S. Kothari Post Doctoral Fellowship (Award letter No. F.4-2/2006(BSR)/MA/17-18/0025) awarded to Dr. Mahvish Ali by the University Grants Commission, Government of India, New Delhi. Publisher Copyright: © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.

PY - 2022/5/26

Y1 - 2022/5/26

N2 - The present work deals with the mathematical investigation of some generalizations of the Szász operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Szász operators involving multiple Sheffer polynomials are considered. Convergence properties of these operators are verified with the help of the universal Korovkin-type result and the order of approximation is calculated by using classical modulus of continuity. Further, the convergence of these operators are also discussed in weighted spaces of functions on the positive semi-axis and estimate the approximation with the help of weighted modulus of continuity. The theoretical results are exemplified choosing the special cases of multiple Sheffer polynomials.

AB - The present work deals with the mathematical investigation of some generalizations of the Szász operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Szász operators involving multiple Sheffer polynomials are considered. Convergence properties of these operators are verified with the help of the universal Korovkin-type result and the order of approximation is calculated by using classical modulus of continuity. Further, the convergence of these operators are also discussed in weighted spaces of functions on the positive semi-axis and estimate the approximation with the help of weighted modulus of continuity. The theoretical results are exemplified choosing the special cases of multiple Sheffer polynomials.

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DO - 10.1007/s41478-022-00443-9

M3 - Article

JO - Journal of Analysis

JF - Journal of Analysis

SN - 0971-3611

ER -

Generalization of Szász operators involving multiple Sheffer polynomials

Abstract

Keywords

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