Korovkin-type theorems and local approximation problems

Of concern are local approximation problems for sequences of positive linear operators acting on linear subspaces of functions defined on a metric space. A Korovkin-type theorem is established in such a framework together with several consequences related to one dimensional, multidimensional and inf...

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Bibliographic Details
Published in:	Expositiones mathematicae Vol. 40; no. 4; pp. 1229 - 1243
Main Author:	Altomare, Francesco
Format:	Journal Article
Language:	English
Published:	Elsevier GmbH 01.12.2022
Subjects:	Bernstein-type operator Bounded [formula omitted] periodic function Convolution operator Korovkin-type theorem Local uniform approximation Positive linear operator secondary Local uniform approximation Korovkin-type theorem Positive linear operator Convolution operator Bounded 2π− periodic function Bernstein-type operator primary
ISSN:	0723-0869, 1878-0792
Online Access:	Get full text
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Summary:	Of concern are local approximation problems for sequences of positive linear operators acting on linear subspaces of functions defined on a metric space. A Korovkin-type theorem is established in such a framework together with several consequences related to one dimensional, multidimensional and infinite dimensional settings (Hilbert spaces). Furthermore, some applications are discussed which concern classical sequences of positive linear operators including (one dimensional and multidimensional) Bernstein operators, Kantorovich operators, Szász–Mirakyan operators, Gauss–Weierstrass operators and Bernstein–Schnabl operators on convex subsets of Hilbert spaces. Finally the paper ends with a reassessment of a result of Korovkin concerning subspaces of bounded 2π− periodic functions on R and with an application related to sequences of convolution operators generated by positive approximate identities.
ISSN:	0723-0869 1878-0792
DOI:	10.1016/j.exmath.2022.06.001