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Statistical Deferred Cesàro Summability and Its Applications to Tauberian Theory

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Abstract

Our aim in this paper is to make a novel interpretation of the relation between the statistical deferred Cesàro summability method and statistical convergence based on a certain subsequence for sequences of real or complex numbers. In line with this aim, we introduce a necessary and sufficient Tauberian condition of Móricz-type for statistically deferred Cesàro summable sequences. In addition, we define the concepts of statistical deferred slow decrease and statistical deferred slow oscillation for a sequence of real and complex numbers, respectively. As a result, we derive some Tauberian conditions controlling \(O_L\)- and O-oscillatory behavior of a sequence in the statistical sense.

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Funding

This study was funded by Türkiye Bilimsel ve Teknolojik Araştirma Kurumu (Grant no. 118C577).

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Author notes

  1. Sefa Anıl Sezer, Zerrin Önder and İbrahim Çanak contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, İstanbul Medeniyet University, 34720, Istanbul, Turkey

    Sefa Anıl Sezer

  2. Department of Mathematics, Ege University, 35100, Izmir, Turkey

    Zerrin Önder & İbrahim Çanak

Authors
  1. Sefa Anıl Sezer
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  2. Zerrin Önder
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  3. İbrahim Çanak
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Correspondence to İbrahim Çanak.

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Communicated by Saeid Maghsoudi.

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Sezer, S.A., Önder, Z. & Çanak, İ. Statistical Deferred Cesàro Summability and Its Applications to Tauberian Theory. Bull. Iran. Math. Soc. 49, 19 (2023). https://doi.org/10.1007/s41980-023-00770-y

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  • DOI: https://doi.org/10.1007/s41980-023-00770-y

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