Studies on λ-statistical convergence of sequences in generalized probabilistic metric spaces

Samiran Das; ARGHA GHOSH

doi:10.5269/bspm.67367

SAMIRAN DAS Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India.
ARGHA GHOSH Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.

Abstract

In this paper, we introduce the notion of λ-statistical convergence of sequences in probabilistic G-metric spaces. We study some basic properties of λ-statistical convergence of sequences. Also introducing the notion of λ-statistically Cauchy sequences, we study its relationship with λ-statistical convergence in probabilistic G-metric spaces. Further, introducing the notion of λ-statistically pre-Cauchy sequences in probabilistic G-metric spaces, we examine the connections among all these new concepts and establish some basic facts.

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