Abel transforms of convolution operators

Abstract

The classical Korovkin approximation theory deals with the convergence of a given sequence {L n } of positive linear operators on C[a,b]. When the sequence of positive linear operators does not converge to the identity operator it may be useful to use some summability methods. In this paper, we study some Korovkin type approximation theorems for the sequences of convolution operators via the Abel method, which is a sequence-to-function transformation. We also deal with the rate of Abel convergence. © 2015 by De Gruyter 2015.