Best Proximity Point Theorems for Asymptotically Relatively Nonexpansive Mappings

DOI10.1080/01630563.2015.1079533zbMath1344.47037arXiv1611.02484OpenAlexW2226172724MaRDI QIDQ2805979

P. Veeramani, Sangem Rajesh

Publication date: 13 May 2016

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

Full work available at URL: https://arxiv.org/abs/1611.02484

zbMATH Keywords

best proximity pointsproperty \(UC\)proximal pairsrelatively nonexpansive mapsasymptotically nonexpansive maps

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Convergence of Picard's iteration using projection algorithm for noncyclic contractions ⋮ Uniform convexity, strong convexity and property UC ⋮ A fixed point theorem for asymptotically nonexpansive type mappings in uniformly convex Banach spaces ⋮ Edelstein’s Theorem for Cyclic Contractive Mappings in Strictly Convex Banach Spaces ⋮ Unnamed Item ⋮ Pythagorean property and asymptotic relatively nonexpansive mappings ⋮ Some results on iterative proximal convergence and Chebyshev center ⋮ Non-convex proximal pair and relatively nonexpansive maps with respect to orbits ⋮ Unnamed Item

Cites Work

• Existence and convergence of best proximity points
• The existence of best proximity points in metric spaces with the property UC
• Best proximity points: approximation and optimization
• On the Structure of Minimal Sets of Relatively Nonexpansive Mappings
• A Note on Existence and Convergence of Best Proximity Points for Pointwise Cyclic Contractions
• Extensions of Edelstein's Theorem on Contractive Mappings
• A new approach to relatively nonexpansive mappings
• Existence and convergence for fixed points of mappings of asymptotically nonexpansive type
• An Introduction to Metric Spaces and Fixed Point Theory
• Proximal normal structure and relatively nonexpansive mappings