Generalized Banach contraction in probabilistic metric/normed spaces

TL;DR

This paper extends classical contraction concepts to probabilistic metric spaces, exploring their properties and broadening the theoretical framework for fixed point theorems in probabilistic contexts.

Contribution

It generalizes B-contraction and C-contraction notions to probabilistic metric spaces and investigates their properties, advancing the understanding of contractions in probabilistic analysis.

Findings

Generalization of B-contraction and C-contraction to probabilistic metric spaces

Analysis of properties of C-contraction within probabilistic metric spaces

Enhanced theoretical foundation for fixed point theorems in probabilistic settings

Abstract

In this paper, we present the generalization of B-contraction and C-contraction due to Sehgal and Hicks respectively. We also study some properties of C-contraction in probabilistic metric space.