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On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces

Author

Listed:
  • Pratulananda Das
  • Kaustubh Dutta
  • Vatan Karakaya

Abstract

We consider the recently introduced notion of ℐ‐statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strong ℐ‐statistical cluster points and extremal limit points, and strong ℐ‐statistical continuity and strong ℐ‐statistical D‐boundedness in probabilistic normed spaces and study some of their important properties.

Suggested Citation

  • Pratulananda Das & Kaustubh Dutta & Vatan Karakaya, 2014. "On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:909364
    DOI: 10.1155/2014/909364
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    References listed on IDEAS

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    1. Pratulananda Das & Kaustubh Dutta & Vatan Karakaya & Sanjoy Ghosal, 2013. "On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    2. Pratulananda Das & Kaustubh Dutta & Vatan Karakaya & Sanjoy Ghosal, 2013. "On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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