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

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