Work

The structure of fuzzy extended $ b $-metric spaces and some fixed-point theorems with applications

Year: 2025

Type: article

Abstract: This paper establishes a novel concept of fuzzy extended $ b $-metric space, which serves as an extension to both fuzzy metric spaces and extended $ b $-metric spaces. The introduction of fuzzy extended $ b $-metric spaces is motivated by the need to model uncertainty and vagueness in real-world problems, where classical metric spaces may fail to capture imprecise relationships. This framework extends traditional $ b $-metric spaces, enhancing their applicability in fuzzy environments and providing a foundation for advanced fixed-point results and applications. By utilizing the extended $ b $-comparison function, some contractive type fixed-point theorems are proved. As an application, we study the homeomorphism between the fuzzy extended $ b $-metric space and the extended $ b $-metric space. In addition, the existence and uniqueness of solutions to the Fredholm integral equation is presented.

Source: AIMS Mathematics

DOI: 10.3934/math.20251351

Authors: Yanrong An, Muhammad Aamir Ali, Jarunee Sirisin, Thanin Sitthiwirattham

Institutions: Nanjing University of Posts and Telecommunications, Hohai University, King Mongkut's University of Technology North Bangkok, Suan Dusit University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: King Mongkut's University of Technology North Bangkok