Best proximity results in metric spaces endowed with a hyperconvex structure

In the current article, we focus on hyperconvex metric spaces and survey the existence of best proximity points and optimal pair of fixed points for cyclic and noncyclic relatively u -continuous mappings which are r -condensing by applying a suitable measure of noncompactness. The method of the proo...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; pp. 25 - 20
Main Authors: Gabeleh, Moosa, Markin, Jack
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 19.09.2025
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Banach spaces
Best proximity point
Differential Geometry
Existence theorems
Hyperconvex metric space
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metric Fixed Point Theory and Its Applications
Metric space
Optimal pair of fixed points
r-condensing operator
Reflexivity
Relatively u-continuous map
Topology
Optimal pair of fixed points
continuous map
47H10
condensing operator
Hyperconvex metric space
51F99
Relatively
Best proximity point
54H25
ISSN:2730-5422, 2730-5422
Online Access:Get full text
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Summary:In the current article, we focus on hyperconvex metric spaces and survey the existence of best proximity points and optimal pair of fixed points for cyclic and noncyclic relatively u -continuous mappings which are r -condensing by applying a suitable measure of noncompactness. The method of the proof of our main results relies on the fact that every hyperconvex metric space ( M , d ) can be isometrically embedded into the Banach space ℓ ∞ ( M ) . Another important tool which will be used in the proof of the existence theorems is to show that the proximal pair of every nonempty and admissible pair in a hyperconvex metric space M is also nonempty and admissible.
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ISSN:2730-5422
2730-5422
DOI:10.1186/s13663-025-00807-3