Fuzzy <i>b</i>-Metric Spaces: Fixed Point Results for <i>ψ</i>-Contraction Correspondences and ItsApplication

• Main Authors: Mujahid Abbas, Fatemeh Lael, Naeem Saleem
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Axioms
• Subjects: fixed point; correspondence; fuzzy b-metric space; b-metric space
• Online Access: https://www.mdpi.com/2075-1680/9/2/36
• ISSN: 2075-1680

In this paper we introduce the concepts of <inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>-contraction and monotone <inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>-contraction correspondence in “fuzzy <inline-formula> <math display="inline"> <semantics> <mi mathvariant="fraktur">b</mi> </semantics> </math> </inline-formula>-metric spaces” and obtain fixed point results for these contractive mappings. The obtained results generalize some existing ones in fuzzy metric spaces and “fuzzy <inline-formula> <math display="inline"> <semantics> <mi mathvariant="fraktur">b</mi> </semantics> </math> </inline-formula>-metric spaces”. Further we address an open problem in <inline-formula> <math display="inline"> <semantics> <mi mathvariant="fraktur">b</mi> </semantics> </math> </inline-formula>-metric and “fuzzy <inline-formula> <math display="inline"> <semantics> <mi mathvariant="fraktur">b</mi> </semantics> </math> </inline-formula>-metric spaces”. To elaborate the results obtained herein we provide an example that shows the usability of the obtained results.