Image of polynomials under generalized Szász operators

Abstract

The motivation behind this paper is a sequence S_n of generalized Szász operators using multiple Appell polynmials. The purpose of the present paper is to find the image of the polynomials under these operators. We find that as n → ∞, S_n (t^m; x) approaches to x^m for every m ∈ ℕ. Finally, We prove the image of a polynomial of degree m under these operators is another polynomial of degree m by using the linearity of these operators.