Korovkin-type approximation for non-positive operators

Fuente: arXiv
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Main Authors: Kumar, V. B. Kiran, Namboodiri, M. N. N., Vinaya, P. C.
Format: Preprint
Published: 2024
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author Kumar, V. B. Kiran
Namboodiri, M. N. N.
Vinaya, P. C.
author_facet Kumar, V. B. Kiran
Namboodiri, M. N. N.
Vinaya, P. C.
contents The classical Korovkin theorem traditionally relies on the positivity of the underlying sequence of operators. However, in 1968, D. E. Wulbert established the first non-positive version. In this article, we generalize Wulbert's result to the class of uniformly bounded sequence of operators. As an application, we obtain an operator version of this Korovkin-type theorem which will cover existing results in this direction. We also present illustrative examples, one of which has its roots in the Grunwald's interpolation operator. In this context, we also present a direct approach with numerical illustrations.
format Preprint
id arxiv_https___arxiv_org_abs_2403_03476
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Korovkin-type approximation for non-positive operators
Kumar, V. B. Kiran
Namboodiri, M. N. N.
Vinaya, P. C.
Functional Analysis
Classical Analysis and ODEs
41A35, 41A36, 41A25, 46B25
The classical Korovkin theorem traditionally relies on the positivity of the underlying sequence of operators. However, in 1968, D. E. Wulbert established the first non-positive version. In this article, we generalize Wulbert's result to the class of uniformly bounded sequence of operators. As an application, we obtain an operator version of this Korovkin-type theorem which will cover existing results in this direction. We also present illustrative examples, one of which has its roots in the Grunwald's interpolation operator. In this context, we also present a direct approach with numerical illustrations.
title Korovkin-type approximation for non-positive operators
topic Functional Analysis
Classical Analysis and ODEs
41A35, 41A36, 41A25, 46B25
url https://arxiv.org/abs/2403.03476