A sequence of positive linear operators associated with an approximation process

Abstract

Considering a general class of discrete linear positive operators, by using a one-to-one function, we associate to the class mentioned above a new sequence of operators. Our aim is to establish the transfer of approximation properties on this construction. The study is carried out in a weighted space and our results are materialized in obtaining both a convergence theorem of Korovkin type and an inequality for the approximation error expressed in terms of a certain weighted modulus of smoothness. Two particular cases are analyzed.