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


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Das P., Dutta K., KARAKAYA V., Ghosal S.

ABSTRACT AND APPLIED ANALYSIS, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2013
  • Doi Number: 10.1155/2013/765060
  • Journal Name: ABSTRACT AND APPLIED ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Yıldız Technical University Affiliated: Yes

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 (Sencimen and Pehlivan, 2008) using ideals and introduce the notion of strong I- and I*-statistical convergence and two related concepts, namely, strong I-lacunary statistical convergence and strong I-lambda-statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.