Convergence Rate of Szász Operators Involving Boas–Buck-Type Polynomials

Abstract

This paper considers a linking of the well-known Szasz operators with the orthogonal polynomials, e.g., Boas–Buck-type polynomials. These polynomials include several important cases such as Brenke-type polynomials, Sheffer polynomials and Appell polynomials. We estimate the approximation degree of these operators for bounded variation functions by applying some methods and techniques of the theory of probability. Further, we extend our study to include the Voronovskaya and Gruss–Voronovskaya-type theorems in the quantitative form by utilizing the order of convergence of the sixth order moment.