The rate of convergence of a generalization of Post–Widder operators and Rathore operators

Abstract

In this paper, we study local approximation properties of certain gamma-type operators. They generalize the Post–Widder operators and the Rathore operators, and approximate locally integrable functions satisfying a certain growth condition on the infinite interval $$[0,\infty )$$ [ 0 , ∞ ) . We derive the complete asymptotic expansion for these operators and prove a localization result. Also, we estimate the rate of convergence for functions of bounded variation.