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


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

ABSTRACT AND APPLIED ANALYSIS, 2013 (SCI İndekslerine Giren Dergi)

  • Basım Tarihi: 2013
  • Doi Numarası: 10.1155/2013/765060
  • Dergi Adı: ABSTRACT AND APPLIED ANALYSIS

Özet

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.