Approximation by a family of summation-integral type operators preserving linear functions

Abstract

This article investigates the approximation properties of a general family of positive linear operators defined on the unbounded interval [0,?). We prove uniform convergence theorem and Voronovskayatype theorem for functions with polynomial growth. More precisely, we study weighted approximation i.e basic convergence theorems, quantitative Voronovskaya-asymptotic theorems and Gr?ss Voronovskayatype theorems in weighted spaces. Finally, we obtain the rate of convergence of these operators via a suitable weighted modulus of continuity.