Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces

DOI10.1016/j.jmaa.2009.01.007zbMath1179.47046OpenAlexW2090780200MaRDI QIDQ1018303

J. Martínez

Publication date: 19 May 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.01.007

zbMATH Keywords

variational inequalitiescommon fixed pointBanach operator pairbest simultaneous approximationasymptotically \((f,g)\)-nonexpansive maps

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (14)

On common fixed points in modular vector spaces ⋮ Banach operator pairs and common fixed points in modular function spaces ⋮ Applications of Caristi's fixed point results ⋮ Common fixed point and approximation results for generalized \((f, g)\)-weak contractions ⋮ Nonexpansive retracts and weak compatible pairs in metric spaces ⋮ Banach operator pairs and common fixed points in hyperconvex metric spaces ⋮ Strong convergence for solving a general system of variational inequalities and fixed point problems in Banach spaces ⋮ One-local retracts and Banach operator pairs in metric spaces ⋮ Existence of common fixed points using Bregman nonexpansive retracts and Bregman functions in Banach spaces ⋮ Common fixed point and invariant approximation results ⋮ Banach operator pair and common fixed points for nonexpansive maps ⋮ Asymptotically pseudocontractions, Banach operator pairs and best simultaneous approximations ⋮ Common fixed point and approximation results for noncommuting maps on locally convex spaces ⋮ Subweakly Biased Pairs and Jungck Contractions with Applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Contractive type non-self mappings on metric spaces of hyperbolic type
• Approximation of fixed points of uniformly \(R\)-subweakly commuting mappings
• Compatible maps and invariant approximations
• Convergence theorems for nonself asymptotically nonexpansive mappings
• Banach operator pairs, common fixed-points, invariant approximations, and \(*\)-nonexpansive multimaps
• Common fixed points for Banach operator pairs with applications
• Common fixed points from best simultaneous approximations
• Fixed point theorems and invariant approximations
• Applications of fixed point theorems to best simultaneous approximations
• On best simultaneous approximation in normed linear spaces
• An application of a fixed-point theorem to approximation theory
• Applications of fixed-point methods to discrete variational and quasi- variational inequalities
• Common fixed points and best approximation
• Approximating common fixed points of asymptotically nonexpansive maps in uniformly convex Banach spaces
• Common fixed-points for Banach operator pairs in best approximation
• Generalized \(I\)-contractions and pointwise \(R\)-subweakly commuting maps
• Common fixed points in best approximation for Banach operator pairs with Ćirić type \(I\)-contractions
• Common fixed point theorems for compatible self-maps of Hausdorff topological spaces
• Common fixed point and invariant approximation results for noncommuting generalized \((f,g)\)-nonexpansive maps
• Common Fixed Points for Commuting and Compatible Maps on Compacta
• A Generalization of Banach's Contraction Principle
• Commuting Mappings and Fixed Points
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings

This page was built for publication: Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces