On the Structure of Minimal Sets of Relatively Nonexpansive Mappings

DOI10.1080/01630563.2013.763824zbMath1285.47062OpenAlexW2068969528MaRDI QIDQ2854327

Moosa Gabeleh, Rafael Espínola

Publication date: 18 October 2013

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2013.763824

zbMATH Keywords

fixed pointbest proximity pointproperty UCrelatively non-expansive mappingproximal normal structure

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (26)

Best proximity points, cyclic Kannan maps and geodesic metric spaces ⋮ A note on best proximity point theory using proximal contractions ⋮ Nonconvex proximal normal structure in convex metric spaces ⋮ Noncyclic $\varphi$-contractions in hyperbolic uniformly convex metric spaces ⋮ Convergence of Picard's iteration using projection algorithm for noncyclic contractions ⋮ On cyclic relatively nonexpansive mappings in generalized semimetric spaces ⋮ Best Proximity Points and Fixed Point Results for Certain Maps in Banach Spaces ⋮ Uniform convexity, strong convexity and property UC ⋮ Common best proximity pairs in strictly convex Banach spaces ⋮ Strong and weak convergence of Ishikawa iterations for best proximity pairs ⋮ Unnamed Item ⋮ Diametrically Relatively Nonexpansive Mappings and a Characterization of Proximal Normal Structure ⋮ Some remarks on convergence of best proximity points and semi-cyclic contractions ⋮ Best Proximity Points and Fixed Points Results for Noncyclic and Cyclic Fisher Quasi-contractions ⋮ Semi-normal structure and best proximity pair results in convex metric spaces ⋮ Remarks on Minimal Sets for Cyclic Mappings in Uniformly Convex Banach Spaces ⋮ On generalized pointwise noncyclic contractions without proximal normal structure ⋮ Some new results on cyclic relatively nonexpansive mappings in convex metric spaces ⋮ Tripartite coincidence-best proximity points and convexity in generalized metric spaces ⋮ A Survey on Best Proximity Point Theory in Reflexive and Busemann Convex Spaces ⋮ Best Proximity Point Theorems for Asymptotically Relatively Nonexpansive Mappings ⋮ Unnamed Item ⋮ Noncyclic mappings and best proximity pair results in Hilbert and uniformly convex Banach spaces ⋮ Common best proximity pairs via the concept of complete proximal normal structure ⋮ Study of minimal invariant pairs for relatively nonexpansive mappings with respect to orbits ⋮ Coincidence best proximity points in convex metric spaces

Cites Work

• Global optimal solutions of noncyclic mappings in metric spaces
• On cyclic Meir-Keeler contractions in metric spaces
• Best proximity points for asymptotic cyclic contraction mappings
• Existence and convergence of best proximity points
• The existence of best proximity points in metric spaces with the property UC
• Existence and uniqueness of best proximity points in geodesic metric spaces
• Convergence and existence results for best proximity points
• Existence of fixed points of nonexpansive mappings in a space without normal structure
• On Best Proximity Points in Metric and Banach Spaces
• A new approach to relatively nonexpansive mappings
• Extensions of Banach's Contraction Principle
• On the integral representation of superbiharmonic functions
• Proximinal Retracts and Best Proximity Pair Theorems
• A Fixed Point Theorem for Mappings which do not Increase Distances
• Proximal normal structure and relatively nonexpansive mappings

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