Fuzzy metric spaces: a survey on fixed point results, contraction principles and simulation functions

Abstract

This paper presents an extensive review of fuzzy metric spaces, with an emphasis on their core topological properties and fixed point theory. It discusses several influential contraction principles that guarantee the existence and uniqueness of fixed points, incorporating the use of auxiliary functions and admissible mappings to enhance these principles. The paper also explores the fuzzy simulation function approach, showcasing its ability to unify various established results within the fuzzy context. This approach not only provides a cohesive framework for understanding the relationships between fixed point theory, contraction mappings, and their interactions within fuzzy metric spaces but also highlights key aspects of fuzzy metric spaces, offering deeper insights into their structure and applications.