Common best proximity point theorems under proximal Fρ♭-weak dominance with application

In partial ♭-metric spaces, we first define F ρ ♭ -weak contraction mappings and develop fixed point theorems in these mappings. In the context of ♭-metric and partial ♭-metric spaces, this study aims to establish the concept of proximally F ρ ♭ -weakly dominated pair of mappings and derive common b...

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Published inFixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; p. 16
Main Authors Ayele, Asaye, Koyas, Kidane
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Commuting
Differential Geometry
Fixed points (mathematics)
Integral equations
Mathematical and Computational Biology
Mathematical functions
Mathematics
Mathematics and Statistics
Metric space
Theorems
Topology
Proximal
Proximally commute
weak dominance
Common best proximity point
Fixed point
Online AccessGet full text
ISSN2730-5422
DOI10.1186/s13663-025-00795-4

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Summary:In partial ♭-metric spaces, we first define F ρ ♭ -weak contraction mappings and develop fixed point theorems in these mappings. In the context of ♭-metric and partial ♭-metric spaces, this study aims to establish the concept of proximally F ρ ♭ -weakly dominated pair of mappings and derive common best proximity point theorems using this pair of mappings. The best proximity point and associated fixed point theorems in the literature are generalized by our new findings. Furthermore, we illustrate our findings with examples. Finally, as evidence for our conclusion, we demonstrate that an integral equation has a solution.
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ISSN:2730-5422
DOI:10.1186/s13663-025-00795-4