Abstract
The aim of this article is to present a general class of positive linear operators of discrete type related to squared fundamental basis functions. If these operators are expressed by a series, we propose to truncate them by a finite sum while still keeping the property of converging towards the identity operator in a weighted space. A relation between the local smoothness of functions and the local approximation is obtained. In the variant in which the operators are described by a finite sum, we establish the limit of their iterates.
Authors
Octavian Agratini
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Keywords
Contraction principle; linear positive operator; Lipschitz function; modulus of smoothness; weighted space
Paper coordinates
O. Agratini, Properties of positive linear operators connected with squared fundamental functions, Numer. Funct. Anal. Optimiz., 45 (2024) no. 2, pp. 103–111, https://doi.org/10.1080/01630563.2024.2316579
About this paper
Journal
Numerical Functional Analysis and Optimization
Publisher Name
Taylor and Francis Ltd.
Print ISSN
15322467
Online ISSN
01630563
google scholar link
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