On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals. (30th September 2013)

• Record Type: Journal Article
• Authors: Das, Pratulananda; Dutta, Kaustubh; Karakaya, Vatan; Ghosal, Sanjoy
• Other Names: Kim Sung Guen Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-09-30
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/765060
• Languages: English
• ISSNs: 1085-3375

Abstract

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 ℐ - and ℐ * -statistical convergence and two related concepts, namely, strong ℐ -lacunary statistical convergence and strong ℐ -λ -statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.