Common Fixed Point Theorem for Six Functions on Menger Probabilistic Generalized Metric Space

TL;DR

This paper establishes a unique common fixed point for six functions within a Menger probabilistic generalized metric space, expanding fixed point theory in probabilistic metric contexts.

Contribution

It introduces compatibility conditions for multiple functions and proves theorems ensuring the existence and uniqueness of common fixed points in this setting.

Findings

Proved theorems guaranteeing fixed points for six functions

Defined compatibility for three functions in probabilistic metric spaces

Extended fixed point results to Menger probabilistic generalized metric spaces

Abstract

The main aim of this paper is to find a unique common fixed point for six functions in a Menger probabilistic generalized metric space. For this purpose, we have defined the compatibility of three functions and established some required theorems.