Fixed Point Property in G-Complete Fuzzy Metric Space

TL;DR

This paper investigates fixed point properties in fuzzy metric spaces by introducing a new contraction condition for multi-valued mappings and extending the results to ordinary metric spaces.

Contribution

It presents a novel contraction condition for fixed points in fuzzy metric spaces and applies the findings to ordinary metric spaces.

Findings

Established existence and uniqueness of fixed points under the new contraction condition

Extended fixed point results from fuzzy metric spaces to ordinary metric spaces

Provided conditions for multi-valued and single-valued mappings

Abstract

Our purpose of this paper is to focus on fixed point property in fuzzy metric space. To achieve our objective, we will introduce a new contraction condition to examine the fixed point for multi-valued mapping, then we will be investigating the obtained result to ensure the existence and uniqueness of this property for single-valued mapping. To show the use of our main result, we will give the relative result in the ordinary metric space.