$A$-statistical convergence for a class of positive linear operators

Abstract

In this paper we introduce a sequence of positive linear operators defined on the space $C[0,a]$ $(0<a<1)$ and provide an approximation theorem for these operators via the concept of $A$-statistical convergence. We also compute the rates of convergence of these approximation operators by means of the first and second order modulus of continuity and the elements of the Lipschitz class. Furthermore, by defining the generalization of $r$-th order of these operators we show that the similar approximation properties are preserved on \(C[0,a].\