Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

Seng Huat OngChoung Min NgYap Hong KeatHari Mohan Srivastava2024-10-222024-10-222022-10-0810.3390/axioms11100537https://dspace-cris.utar.edu.my/handle/123456789/4210The 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 Szász–Mirakyan operator averaged by a certain probability distribution.Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operatorsjournal-article