Some probabilistic generalizations of the Cheney-Sharma and Bernstein approximation operators

Authors

• Seng Huat OngFollow
• Choung Min NgFollow
• Hong Keat Yap
• Hari Mohan Srivastava

Document Type

Article

Publication Date

10-1-2022

Abstract

The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined. The convergence property of the Bernstein generalization is established. It is also shown that the Cheney-Sharma operator is the Szasz-Mirakyan operator averaged by a certain probability distribution.

Keywords

Generalized Laguerre polynomials, Korovkin theorem, noncentral negative binomial, Probabilistic derivation, Weierstrass approximation theorem, Szasz-Mirakyan operator

Publication Title

Axioms

Recommended Citation

Ong, Seng Huat; Ng, Choung Min; Yap, Hong Keat; and Srivastava, Hari Mohan, "Some probabilistic generalizations of the Cheney-Sharma and Bernstein approximation operators" (2022). Research Publications (2021 to 2025). 1418.
https://knova.um.edu.my/research_publications_2021_2025/1418

Divisions

Science

Funders

[FRGS/1/2020/STG06/SYUC/02/1]

Volume

11

Issue

10

Publisher

MDPI

Publisher Location

ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND