Generalized Szász Durrmeyer operators

Abstract

In this paper, we introduce and study a new sequence of positive linear operators acting on the spaces of continuous function on positive semi-axis. These operators are defined by means of the q-integral, which generalize the Szász Durrmeyer operators. We study their approximation property by presenting a direct approximation theorem on polynomial weighted spaces and the rate of convergence by means of weighted modulus of continuity. Also, we establish an asymptotic formula with respect to weighted norm. © 2011 Pleiades Publishing, Ltd.