Korovkin theorems on weighted spaces: revisited
type: Item
instance of: scholarly article
title: Korovkin theorems on weighted spaces: revisited
zbMATH Open document ID: 1399.41039
author: Mehmet Ünver
author: Oktay Duman
author: Özlem Girgin Atlıhan
published in: Periodica Mathematica Hungarica
publication date: 2018-03-16T00:00:00Z
review text: The paper contains new, direct and easy proofs of the Korovkin theorems for positive linear operators acting on weighted spaces. An important tool is a lemma of \textit{A. D. Gadziev} [Mat. Zametki 20, 781--786 (1976; Zbl 0383.41016)]. Using it, the authors revise the proofs of some of their earlier results. First, the ordinary approximation process by positive linear operators acting between weighted spaces is investigated and quantitative results are obtained. Then applications and examples are given, using different notions of convergence, such as statistical convergence, summation processes, Abel's method.
reviewed by: Ioan Raşa
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 40G15
Mathematics Subject Classification ID: 40C15
zbMATH DE Number: 6851243
zbMATH Keywords: weighted approximation
zbMATH Keywords: Korovkin theorem
zbMATH Keywords: statistical convergence
zbMATH Keywords: summation process
zbMATH Keywords: Abel summability
MaRDI profile type: Publication
full work available at URL: s10998-017-0187-y
OpenAlex ID: W2616016905
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DOI: 10.1007/S10998-017-0187-Y
description: scientific article; zbMATH DE number 6851243