descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2010Publisher:University of Debrecen/ Debreceni EgyetemJournal:Publicationes Mathematicae Debrecen, volume 76, pages 77-88 (issn: 0033-3883,

Authors: Khan, Mohammad Kazim; Orhan, Cihan;

doi: 10.5486/pmd.2010.4346

Characterizations of strong and statistical convergences

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Abstract

Summary: The two main objectives of the paper are firstly to cast the concept of \(A\)-uniform integrability in the measure-theoretic sense, leading to showing that a sequence is \(A\)-strongly convergent if and only if it is \(A\)-statistically convergent and it is \(A\)-uniformly integrable. The second aim is to give an almost all subsequence characterization of \(A\)-statistical convergence.

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Keywords

strong convergence, summability of subsequences, Summability methods using statistical convergence, \(A\)-uniform integrability, statistical convergence, Absolute and strong summability, Inclusion and equivalence theorems in summability theory

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