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On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals

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  • Pratulananda Das
  • Kaustubh Dutta
  • Vatan Karakaya
  • Sanjoy Ghosal

Abstract

Following the line of (Das et al., 2011, Savas and Das, 2011), we make a new approach in this paper to extend the notion of strong convergence and more general strong statistical convergence (Şençimen and Pehlivan, 2008) using ideals and introduce the notion of strong - and -statistical convergence and two related concepts, namely, strong -lacunary statistical convergence and strong - -statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:765060
    DOI: 10.1155/2013/765060
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