Fixed points of multiplicative contraction mappings on multiplicative metric spaces

TL;DR

This paper explores fixed point theorems for multiplicative contraction mappings within multiplicative metric spaces, demonstrating that the positive real numbers form a complete space under this metric.

Contribution

It introduces the concept of multiplicative contraction mappings and proves fixed point theorems in the context of multiplicative metric spaces, extending classical fixed point theory.

Findings

The set of positive real numbers is a complete multiplicative metric space.

Fixed point theorems for multiplicative contraction mappings are established.

The results generalize classical fixed point theorems to multiplicative metric spaces.

Abstract

In this paper, we first discussed multiplicative metric mapping by giving some topological properties of the relevant multiplicative metric space. As an interesting result of our discussions, we observed that the set of positive real numbers $\mathbb{R}_+$ is a complete multiplicative metric space with respect to the multiplicative absolute value function. Furthermore, we introduced concept of multiplicative contraction mapping and proved some fixed point theorems of such mappings on complete multiplicative metric spaces