Garrancho, PedroMartínez-Sánchez, Francisco-JavierCárdenas-Morales, Daniel2024-09-092024-09-092024-02P. Garrancho, F.-J. Martínez-Sánchez, D. Cárdenas-Morales, Approximation rate and saturation under generalized convergence, Mathematical Foundations of Computing 2024, Volume 7, Issue 1: 148-157.2577-883810.3934/mfc.2023002https://hdl.handle.net/10953/3181This article has been published in a revised form in Mathematical Foundations of Computing http://dx.doi.org/10.3934/mfc.2023002. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative worksIn 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.engKorovkin-type resultsGeneralized convergenceSaturation classinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess