Abstract and Applied Analysis

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

Pratulananda Das, Kaustubh Dutta, Vatan Karakaya, and Sanjoy Ghosal

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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 - λ -statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 765060, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512062

Digital Object Identifier
doi:10.1155/2013/765060

Mathematical Reviews number (MathSciNet)
MR3108647

Zentralblatt MATH identifier
07095345

Citation

Das, Pratulananda; Dutta, Kaustubh; Karakaya, Vatan; Ghosal, Sanjoy. On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals. Abstr. Appl. Anal. 2013 (2013), Article ID 765060, 8 pages. doi:10.1155/2013/765060. https://projecteuclid.org/euclid.aaa/1393512062


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