Asymptotically lacunary µ-statistical equivalence of generalized difference sequences in probabilistic normed spaces

Abstract

The current article introduces the notion of asymptotically lacunary $(\Delta^n,\mu)$-statistical equivalent sequence in the settings of a probabilistic norm $N$. Furthermore, the article presents the concepts of asymptotically $(\Delta^n,\mu)$-strongly Ces\'{a}ro equivalent sequences and asymptotically $(\Delta^n,\mu)$-strongly Ces\'{a}ro Orlicz equivalent sequences in the theory of probabilistic normed spaces and also investigates their various properties including some inclusion relations as well as some equivalent conditions in this new settings.