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Subsequential Convergence Conditions

Abstract

Let be a sequence of real numbers and let be any regular limitable method. We prove that, under some assumptions, if a sequence or its generator sequence generated regularly by a sequence in a class of sequences is a subsequential convergence condition for, then for any integer, the repeated arithmetic means of,, generated regularly by a sequence in the class, is also a subsequential convergence condition for.

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Correspondence to İbrahim Çanak.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Çanak, İ., Totur, Ü. & Dik, M. Subsequential Convergence Conditions. J Inequal Appl 2007, 087414 (2007). https://doi.org/10.1155/2007/87414

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Keywords

  • Generator Sequence
  • Real Number
  • Convergence Condition
  • Limitable Method
  • Arithmetic Means
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