On best proximity pair theorems for relatively \(u\)-continuous mappings

DOI10.1016/j.na.2011.02.021zbMath1217.54044OpenAlexW1987282029MaRDI QIDQ544151

A. Anthony Eldred, V. Sankar Raj, P. Veeramani

Publication date: 14 June 2011

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.2011.02.021

zbMATH Keywords

affine mappingsmetric projectionbest proximity pointscommon best proximity pointsrelatively \(u\)-continuous mappings

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (14)

On best proximity points of upper semicontinuous multivalued mappings ⋮ Best proximity point theorems for \(\alpha\)-nonexpansive mappings in Banach spaces ⋮ Common best proximity point theorems: global minimization of some real-valued multi-objective functions ⋮ Markov-Kakutani's theorem for best proximity pairs in Hadamard spaces ⋮ Relative Continuity, Proximal Boundedness and Best Proximity Point Theorems ⋮ Common best proximity pairs in strictly convex Banach spaces ⋮ Best proximity point results in geodesic metric spaces ⋮ Generalized Acyclic Contractions, Acyclic Contractions, and Reverse Acyclic Contractions ⋮ A characterization of strictly convex spaces and applications ⋮ Pythagorean property and asymptotic relatively nonexpansive mappings ⋮ Condensing mappings and best proximity point results ⋮ Noncyclic Meir-Keeler contractions and best proximity pair theorems ⋮ Best approximation theorems for almost cyclic contractions ⋮ Best proximity points for relatively \(u\)-continuous mappings in Banach and hyperconvex spaces

Cites Work

• Existence of best proximity pairs and equilibrium pairs
• Existence and convergence of best proximity points
• Best approximation theorems for nonexpansive and condensing mappings in hyperconvex spaces
• Convergence and existence results for best proximity points
• Proximal pointwise contraction
• On existence of equilibrium pair for constrained generalized games
• On general best proximity pairs and equilibrium pairs in free abstract economies
• Extensions of two fixed point theorems of F. E. Browder
• Best proximity pair theorems for relatively nonexpansive mappings
• Proximinal Retracts and Best Proximity Pair Theorems
• Zum Prinzip der kontraktiven Abbildung
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• A Fixed Point Theorem for Mappings which do not Increase Distances
• Proximal normal structure and relatively nonexpansive mappings
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