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 involving the beta function and the Boas-Buck-Sheffer polynomials, and compute the convergence error of these operators using the first and second modulus of continuities. We give approximation properties in weighted space and we give a global error estimate in Lipschitz type space. We also construct a sequence of bivariate extensions of these operators and give the rate of convergence using the partial and full modulus of continuities. In addition, some examples, including graphs, are given for one-and two-variable functions to visually illustrate convergence to a function.