Mutually nearest and farthest points of sets and the drop theorem in geodesic spaces

DOI10.1007/S00605-010-0266-0zbMath1238.41017OpenAlexW2032532023MaRDI QIDQ662410

Adriana Nicolae, Rafael Espínola

Publication date: 22 February 2012

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/xmlui/handle/11441/43923

zbMATH Keywords

minimization problemwell-posednessbest approximationgeodesic spacemaximization problemdrop theorem

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

Related Items (8)

Best proximity point (pair) results via MNC in Busemann convex metric spaces ⋮ Markov-Kakutani's theorem for best proximity pairs in Hadamard spaces ⋮ Best Proximity Pair Results for Relatively Nonexpansive Mappings in Geodesic Spaces ⋮ Diametrically Relatively Nonexpansive Mappings and a Characterization of Proximal Normal Structure ⋮ Mappings of generalized condensing type in metric spaces with Busemann convex structure ⋮ Pythagorean property and asymptotic relatively nonexpansive mappings ⋮ A Survey on Best Proximity Point Theory in Reflexive and Busemann Convex Spaces ⋮ Condensing operators of integral type in Busemann reflexive convex spaces

Cites Work

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• Well-posed optimization problems
• Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
• A concept of convergence in geodesic spaces
• Nearest and farthest points in spaces of curvature bounded below
• The strong Ekeland variational principle, the strong drop theorem and applications
• On mutually nearest and mutually furthest points of sets in Banach spaces
• On the cut locus in Alexandrov spaces and applications to convex surfaces
• On mutually nearest and mutually farthest points in reflexive Banach spaces
• Proximinality in geodesic spaces
• Extending Stechkin's theorem and beyond
• Geometric properties of Banach spaces and the existence of nearest and farthest points
• Fixed points of uniformly Lipschitzian mappings
• Reductive groups over a local field
• The drop theorem, the petal theorem and Ekeland's variational principle
• Porous Sets in Best Approximation Theory
• Remotality of Closed Bounded Convex Sets in Reflexive Spaces
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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