Approximation by k-th order modifications of Szász-Mirakyan operators

Abstract

In this paper, we study the k-th order Kantorovich type modication of Szasz-Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szasz-Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.