Abel transforms of positive linear operators on weighted spaces

Abstract

The classical Korovkin approximation theory deals with the convergence of a sequence of positive linear operators. When the sequence of positive linear operators does not converge it will be useful to use some summability methods. In this paper we use the Abel method, a sequence-to-function transformation, to study a Korovkin type approximation theorem for positive linear operators acting from a weighted space $C_{\rho_{1}}$ into a weighted space $B_{\rho_{2}}.$ Moreover using the modulus of continuity we also give rate of Abel convergence.