Approximation Results for the Operators Involving Beta Function and the Boas-Buck-Sheffer Polynomials

Abstract

In this study, we consider a sequence of linear positive operators which involves beta function and the Boas-Buck-Sheffer polynomials and compute the error of convergence of them with the help of the first and the second modulus of continuities. We state approximation properties in weighted space and we
state a global error estimation in Lipschitz type space. Also, we construct a sequence of bivariate extension of these operators and give the rate of convergence by means of partial and full modulus of continuities.
Moreover, some examples including graphs are given for one and two variable functions to illustrate the convergence to a function visually.