Extension of Nörlund and Riesz means: new estimates

Jorge Bustamante                <meta name=

2022/101/1-2 (13) — DOI: 10.5486/PMD.2022.9286 — pp. 231-257

Extension of Nörlund and Riesz means: new estimates

Authors: Jorge Bustamante and Lázaro Flores-de-Jesús

Abstract:

In this paper, we present several new results related with the approximation of functions in $\mathbb{L}^p$, $1\leq p\leq \infty$, by Nörlund and Riesz type operators. We prove that the errors can be measured in terms of Fejér operators and provided specific constants. Some known facts are improved.

Keywords: Nörlund and Riesz operators, Fejér operators, approximation of Lipschitz type functions, rate of convergence

Mathematics Subject Classification: 42A24, 41A25, 42A10