Exploring Proinov-type and Banach-type contractions in fuzzy bipolar metric spaces

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 94 - 20
• Main Authors: Wong, Koon Sang, Salleh, Zabidin, Akhadkulov, Habibulla, Kuljanov, Utkir Nematovich
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Banach contraction; Fixed point; Fixed points (mathematics); Fuzzy bipolar metric space; Fuzzy sets; Integral equation; Integral equations; Mathematicians; Mathematics; Mathematics and Statistics; Metric space; Proinov contraction; Banach contraction; 47H10; Proinov contraction; Fuzzy bipolar metric space; Integral equation; Fixed point; 54H25
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-025-03344-0

Banach-type contractions have played an important role in fixed point theory. Recently, the newly introduced Proinov-type contractions have gained attention due to their wide applicability under various conditions. However, the study of these contractions in newly proposed generalized fuzzy metric spaces remains insufficiently explored. In this paper, we conduct an in-depth exploration of generalized Proinov-type and Banach-type contractions in the context of fuzzy bipolar metric spaces, a generalization of fuzzy metric spaces. We discuss several fixed-point findings for these contractions and provide illustrative examples. Importantly, our findings contribute to the resolution of previously open questions. Furthermore, we showcase the practical applicability of our results in solving integral equations.