Summability methods in weighted approximation to derivatives of functions

Abstract

In this paper, we use summability methods on the approximation to derivatives of functions by a family of linear operators acting on weighted spaces. This point of view enables us to overcome the lack of ordinary convergence in the approximation. To support this idea, at the end of the paper, we will give a sequence of positive linear operators obeying the arithmetic mean approximation (or, approximation with respect to the Ces`aro method) although it is impossible in the usual sense. Some graphical illustrations are also provided.