Some probabilistic generalizations of the Cheney-Sharma and Bernstein approximation operators
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
Divisions
Science
Funders
[FRGS/1/2020/STG06/SYUC/02/1]
Publication Title
Axioms
Volume
11
Issue
10
Publisher
MDPI
Publisher Location
ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND
COinS