Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

DOI10.1090/S0002-9939-01-06141-XzbMath0985.47041OpenAlexW1523814173MaRDI QIDQ2750850

P. Lorenzo Ramírez, Domínguez Benavides, Tomás

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06141-x

zbMATH Keywords

retractioncommon fixed pointasymptotically nonexpansive mapconvergence of iterates

Mathematics Subject Classification ID

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

Related Items

Fixed point property for general topologies in some Banach spaces ⋮ Virtually stable maps and their fixed point sets ⋮ Virtually nonexpansive maps and their convergence sets ⋮ Some geometric properties in modular spaces and application to fixed point theory ⋮ Strong convergence theorems for semigroups of asymptotically nonexpansive mappings in Banach spaces ⋮ On fixed-point sets of nonexpansive mappings in nonstandard hulls and Banach space ultrapowers ⋮ The structure of fixed-point sets of Lipschitzian type semigroups ⋮ Fixed points of asymptotically nonexpansive type mappings ⋮ Geometrical coefficients and the structure of the fixed-point set of asymptotically regular mappings in Banach spaces ⋮ Fixed point sets through iteration schemes ⋮ The structure of fixed-point sets of uniformly Lipschitzian semigroups ⋮ One-local retracts and Banach operator pairs in metric spaces ⋮ Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings ⋮ The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces ⋮ Fixed point, approximate fixed point and Kantorovich--Rubinstein maximum principle in convex metric spaces ⋮ Existence of ergodic retractions for semigroups in Banach spaces ⋮ Existence and approximation of fixed points of nonlinear mappings in spaces with weak uniform normal structure ⋮ Ergodic retractions for families of asymptotically nonexpansive mappings ⋮ Existence of fixed points for asymptotically nonexpansive type actions of semigroups ⋮ Remarks on the structure of the fixed-point sets of uniformly Lipschitzian mappings in uniformly convex Banach spaces ⋮ The retractions onto the common fixed points of some families and semigroups of mappings ⋮ The methods of Hilbert spaces and structure of the fixed-point set of Lipschitzian mapping ⋮ Existence of fixed points and retractions for asymptotically nonexpansive semigroups in locally convex spaces ⋮ Fixed point sets of set-valued mappings ⋮ Some Fixed Point Results for Commuting Families of Mappings in Modular Spaces ⋮ Structure of the fixed point set of asymptotically nonexpansive mappings in Banach spaces with weak uniformly normal structure

Cites Work

• Unnamed Item
• Unnamed Item
• A common fixed point theorem for a commuting family of nonexpansive mappings
• Remarks on asymptotically nonexpansive mappings
• Asymptotic behavior of nonexpansive mappings
• An Asymptotically Nonexpansive Commutative Semigroup with no Fixed Points
• Existence and convergence for fixed points of mappings of asymptotically nonexpansive type
• Stability of weak normal structure in James quasi reflexive space
• Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
• A fixed point theorem on k-uniformly rotund spaces
• Uniformly Lipschitzian Families of Transformations in Banach Spaces
• Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings
• Asymptotic behavior for asymptotically nonexpansive mappings
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Properties of Fixed-Point Sets of Nonexpansive Mappings in Banach Spaces