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Abstract and Applied Analysis
Volume 2013, Article ID 765060, 8 pages
http://dx.doi.org/10.1155/2013/765060
Research Article

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

1Department of Mathematics, Jadavpur University, Kolkata 700032, India
2Department of Mathematical Engineering, Yıldız Technical University, Esenler, Istanbul 34210, Turkey
3Department of Mathematics, Kalyani Government Engineering College, Kalyani, Nadia 741235, India

Received 21 June 2013; Accepted 5 September 2013

Academic Editor: Sung Guen Kim

Copyright © 2013 Pratulananda Das et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.