Existence and uniqueness of best proximity points in geodesic metric spaces

DOI10.1016/j.na.2010.04.005zbMath1196.54050OpenAlexW2073643781MaRDI QIDQ984061

Aurora Fernández-León

Publication date: 13 July 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.04.005

zbMATH Keywords

best proximity pointstrictly convex metric spacegeodesic metric spacecyclic contraction

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Special maps on metric spaces (54E40)

Related Items (17)

Best proximity points, cyclic Kannan maps and geodesic metric spaces ⋮ \(p-\)cyclic \(C\)-contraction result in Menger spaces using a control function ⋮ Common best proximity point theorems: global minimization of some real-valued multi-objective functions ⋮ Best Proximity Pair Results for Relatively Nonexpansive Mappings in Geodesic Spaces ⋮ Best proximity point theorems: resolution of an important non-linear programming problem ⋮ On cyclic Meir-Keeler contractions in metric spaces ⋮ Some results on best proximity points ⋮ Best proximity point results in geodesic metric spaces ⋮ A characterization of proximal normal structure via proximal diametral sequences ⋮ Best proximity point results for MK-proximal contractions ⋮ Best proximity point theorems: an exploration of a common solution to approximation and optimization problems ⋮ Generalized Acyclic Contractions, Acyclic Contractions, and Reverse Acyclic Contractions ⋮ Seminormal structure and fixed points of cyclic relatively nonexpansive mappings ⋮ Global optimization in metric spaces with partial orders ⋮ On the Structure of Minimal Sets of Relatively Nonexpansive Mappings ⋮ Best Proximity Points ⋮ Some results on best proximity points of cyclic Meir-Keeler contraction mappings

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• An Introduction to Metric Spaces and Fixed Point Theory
• Proximal normal structure and relatively nonexpansive mappings
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• Some geometric and topological properties of the unit ball in Banach spaces

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