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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Vydáno v:Expositiones mathematicae Ročník 40; číslo 4; s. 1229 - 1243
Hlavní autor: Altomare, Francesco
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier GmbH 01.12.2022
Témata:
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
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Popis
Shrnutí: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