Approximation rate and saturation under generalized convergence

Abstract

In this paper we prove a quantitative result about the convergence of sequences of functions de ned from linear operators. The notion of conver- gence used here is the one given in [8]. The operators will be assumed to satisfy a shape preserving property associated with certain generalized deriv- ative. We also study the saturation class, from the asymptotic condition that the sequence of operators ful lls. Finally, as applications, we show how the notion of weighted g-statistical convergence, recently studied by A. Adem and M. Altinok [3], can be moved to the setting of approximation theory. Besides, we give a non standard example that shows the applicability of the results.