On Cluster Points, Continuity, and Boundedness Associated with the Generalized Statistical Convergence in Probabilistic Normed Spaces

Abstract

We consider the recently introduced notion of $ℐ$-statistical convergence (Das, Savas and Ghosal, Appl. Math. Lett., 24(9) (2011), 1509–1514, Savas and Das, Appl. Math. Lett. 24(6) (2011), 826–830) in probabilistic normed spaces and in the following (Şençimen and Pehlivan (2008 vol. 26, 2008 vol. 87, 2009)) we introduce the notions like strong $ℐ$-statistical cluster points and extremal limit points, and strong $ℐ$-statistical continuity and strong $ℐ$-statistical D-boundedness in probabilistic normed spaces and study some of their important properties.