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Strong Γ-Statistical Convergence in Probabilistic Normed Spaces

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Abstract

The concept of statistical cluster point of a sequence which presents random deviations is very important in the study of optimal paths and turnpike theory. In this study, we investigate some properties of the set of all strong statistical cluster points of a sequence in a probabilistic normed (PN) space in which the norms of the vectors are represented by probability distribution functions due to randomness. In this context, we also introduce the concept of strong Γ-statistical convergence in a PN space, and examine some of its basic properties.

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Authors and Affiliations

  1. Department of Mathematics, Mehmet Akif Ersoy University Faculty of Arts and Sciences, İstiklal Campus, 15030, Burdur, Turkey

    Celaleddin Şençimen

  2. Department of Mathematics, Süleyman Demirel University Faculty of Arts and Sciences, East Campus, 32260, Isparta, Turkey

    Serpil Pehlivan

Authors
  1. Celaleddin Şençimen
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  2. Serpil Pehlivan
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Correspondence to Celaleddin Şençimen.

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Şençimen, C., Pehlivan, S. Strong Γ-Statistical Convergence in Probabilistic Normed Spaces. Acta Math Vietnam 41, 595–606 (2016). https://doi.org/10.1007/s40306-015-0158-4

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  • DOI: https://doi.org/10.1007/s40306-015-0158-4

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