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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Vydáno v:Fixed point theory and algorithms for sciences and engineering Ročník 2025; číslo 1; s. 25 - 20
Hlavní autoři: Gabeleh, Moosa, Markin, Jack
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 19.09.2025
Springer Nature B.V
SpringerOpen
Témata:
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
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Abstract 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.
AbstractList 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.
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.
Abstract 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 ) $(\mathcal {M}, d)$ can be isometrically embedded into the Banach space ℓ ∞ ( M ) $\ell ^{\infty}(\mathcal {M})$ . 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 $\mathcal {M}$ is also nonempty and admissible.
ArticleNumber 25
Author Markin, Jack
Gabeleh, Moosa
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Keywords Optimal pair of fixed points
continuous map
47H10
condensing operator
Hyperconvex metric space
51F99
Relatively
Best proximity point
54H25
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Snippet 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...
Abstract 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...
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SubjectTerms 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
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Title Best proximity results in metric spaces endowed with a hyperconvex structure
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Volume 2025
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