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Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

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Abstract

In (Çanak and Totur, Georgian Math J 23(1):33–42, 2016), Çanak and Totur have extended some classical Tauberian theorems for single sequences to triple sequences. In (Fridy and Khan, Proc Am Math Soc 128:2347–2355, 2000), Fridy and Khan obtained statistical extensions of some classical Tauberian theorems. The concept of statistical convergence for triple sequences has been introduced by Şahiner et al. (Selcuk J Appl Math 8(2):49–55, 2007). In this paper, we investigate Tauberian conditions for the statistical convergence and statistical (C,1,1,1) summability of triple sequences.

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Authors and Affiliations

  1. Department of Mathematics, Ege University, İzmir, Turkey

    İbrahim Çanak & Zerrin Önder

  2. Department of Mathematics, Adnan Menderes University, Aydin, Turkey

    Ümit Totur

Authors
  1. İbrahim Çanak
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  2. Zerrin Önder
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  3. Ümit Totur
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Correspondence to İbrahim Çanak.

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Çanak, İ., Önder, Z. & Totur, Ü. Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences. Results. Math. 70, 457–473 (2016). https://doi.org/10.1007/s00025-016-0582-3

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  • DOI: https://doi.org/10.1007/s00025-016-0582-3

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