@article{An2025, 
author = {Yanrong An and Muhammad Aamir Ali and Jarunee Sirisin and Thanin Sitthiwirattham},
title = {The structure of fuzzy extended    b-metric spaces and some fixed-point theorems with applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {30785-30805},
keywords = {fuzzy extended b-metric space, fixed point theorem, homeomorphism},
url = {https://www.sciopen.com/article/10.3934/math.20251351},
doi = {10.3934/math.20251351},
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.}
}