Construction of Fixed Points for Asymptotically Nonexpansive Mappings

DOI10.2307/2043667zbMath0489.47035OpenAlexW4243677829MaRDI QIDQ3951113

G.Passty

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/2043667

zbMATH Keywords

fixed point setcommon fixed pointsasymptotically nonexpansive self-mapsuniformly convex Banach space with a Frechet differentiable norm

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (24)

Strong and weak convergence theorems for asymptotically nonexpansive mappings. ⋮ On the convergence of iteration processes for semigroups of nonlinear mappings in modular function spaces ⋮ Existence and convergence for fixed points of mappings of asymptotically nonexpansive type ⋮ A Nonlinear Ergodic Theorem for a Reversible Semigroup of Lipschitzian Mappings in a Hilbert Space ⋮ Approximating a common fixed point of finite family of asymptotically quasi-nonexpansive mappings in Banach spaces ⋮ Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings ⋮ Fixed point iteration processes for asymptotic pointwise nonexpansive mapping in modular function spaces ⋮ Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings ⋮ Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces ⋮ Weak and strong convergence to fixed points of asymptotically nonexpansive mappings ⋮ Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces ⋮ A new convergence theorem for families of asymptotically nonexpansive maps and solution of variational inequality problem ⋮ Asymptotic behavior of almost-orbits of reversible semigroups of Lipschitzian mappings ⋮ Unnamed Item ⋮ A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings ⋮ A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings ⋮ Approximating fixed points of total asymptotically nonexpansive mappings ⋮ On the set of common fixed points of semigroups of nonlinear mappings in modular function spaces ⋮ Fixed Point Iteration Processes for Asymptotically Nonexpansive Mappings ⋮ Iterative approximation of fixed points of (asymptotically) nonexpansive mappings ⋮ Asymptotically nonexpansive mappings in modular function spaces ⋮ Iterative approaches to common fixed points of asymptotically nonexpansive mappings ⋮ A nonlinear ergodic theorem for asymptotically nonexpansive mappings in Banach spaces ⋮ A new composite implicit iterative algorithm for nonself asymptotically nonexpansive mappings

Cites Work

• Über die Methode sukzessiver Approximationen
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak Convergence to the Fixed Point of an Asymptotically Nonexpansive Map
• A Nonlinear Theorem of Ergodic Type
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Unnamed Item

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