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Lacunary ideal summability and its applications to approximation theorem

Lacunary ideal summability and its applications to approximation theorem An ideal I is a family of subsets of positive integers $$\mathbf {N}$$ N which is closed under taking finite unions and subsets of its elements. In this paper, we define and study the notion of $$I_{\theta }$$ I θ -convergence as a variant of the notion of ideal convergence, where $$\theta = (h_{r})$$ θ = ( h r ) is a nondecreasing sequence of positive real numbers. We further apply this notion of summability to prove a Korovkin type approximation theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Lacunary ideal summability and its applications to approximation theorem

The Journal of Analysis , Volume 27 (4) – Dec 7, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-018-0158-6
Publisher site
See Article on Publisher Site

Abstract

An ideal I is a family of subsets of positive integers $$\mathbf {N}$$ N which is closed under taking finite unions and subsets of its elements. In this paper, we define and study the notion of $$I_{\theta }$$ I θ -convergence as a variant of the notion of ideal convergence, where $$\theta = (h_{r})$$ θ = ( h r ) is a nondecreasing sequence of positive real numbers. We further apply this notion of summability to prove a Korovkin type approximation theorem.

Journal

The Journal of AnalysisSpringer Journals

Published: Dec 7, 2018

References