A common fixed point theorem for two self-mappings defined on strictly convex probabilistic cone metric space

TL;DR

This paper introduces a fixed point theorem for two self-mappings in strictly convex probabilistic cone metric spaces, utilizing topological methods to handle nondeterministic distances and providing illustrative examples.

Contribution

It presents a novel shared fixed point theorem for two self-mappings in strictly convex probabilistic cone metric spaces, expanding fixed point theory in probabilistic metric spaces.

Findings

Established a shared fixed point theorem for two self-mappings.

Demonstrated the use of topological methods in probabilistic metric spaces.

Provided multiple examples to validate theoretical results.

Abstract

This study focuses on defining normal and strictly convex structures within Menger cone PM-space. It also presents a shared fixed point theorem for the existence of two self-mappings constructed on a strictly convex probabilistic cone metric space. The core finding is demonstrated through topological methods to describe spaces with nondeterministic distances. To strengthen our conclusions, we provide several examples. In this research, we introduce and explore normal and strictly convex structures in Menger cone PM-space. A significant contribution of our work is the presentation of a shared fixed point theorem concerning the existence of two self-mappings on a strictly convex probabilistic cone metric space. This theorem is substantiated through topological approaches that effectively describe spaces characterized by nondeterministic distances. To further validate our conclusions, we supplement our theoretical findings with a series of illustrative examples. Our study delves into the intricacies of normal and strictly convex structures within Menger cone PM-space. We present a shared fixed point theorem, demonstrating the existence of two self-mappings in a strictly convex probabilistic cone metric space. Employing topological approaches, we elucidate the key finding and describe spaces with nondeterministic distances. To support and enhance the robustness of our conclusions, we include a variety of examples throughout the study.