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A generalized statistical convergence via ideals - MaRDI portal

A generalized statistical convergence via ideals (Q2430032)

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A generalized statistical convergence via ideals
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    A generalized statistical convergence via ideals (English)
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    5 April 2011
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    The notion of \(\lambda\)-statistical convergence was introduced by \textit{Mursaleen} [Math. Slovaca 50, No.~1, 111--115 (2000; Zbl 0953.40002)] as an extension of the \([V, \lambda]\) summability of \textit{L. Leindler} [Publ. Math. 10, 274--282 (1964; Zbl 0129.05002)]. The authors introduce the concepts of \(I\)-\([V, \lambda]\)-summability and \(I\)-\(\lambda\)-statistical convergence by using ideals. They study the relation between these newly defined methods as well as the relation between \(I\)-\(\lambda\)-statistical convergence and \(I\)-statistical convergence.
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    ideal
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    filter
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    \(I\)-statistical convergence
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    \(I\)-\(\lambda\)-statistical convergence
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    \(I\)-\([V, \lambda]\)-summability
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    closed subspace
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