Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings

DOI10.1016/0362-546X(94)00128-5zbMath0865.47040OpenAlexW2040851960MaRDI QIDQ4839226

Kok-Keong Tan, Pei-Kee Lin, Hong-Kun Xu

Publication date: 17 July 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)00128-5

zbMATH Keywords

Banach spacesuniformly convex Banach spacefixed point propertyOpial modulusdemiclosedness principleLipschitzian semigroupnearly uniformly convex Banach spaceasymptotically nonexpansive mapsweakly compact convex subsetsBynum's weakly convergent sequence coefficientlocally uniform Opial condition

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

Fixed point theorems for mappings of asymptotically nonexpansive type ⋮ Smoothness, asymptotic smoothness and the Blum-Hanson property ⋮ Some remarks on the set of common fixed points of one-parameter semigroups of nonexpansive mappings in Banach spaces with the Opial property ⋮ Shrinking projection methods for solving split equilibrium problems and fixed point problems for asymptotically nonexpansive mappings in Hilbert spaces ⋮ Asymptotically nonexpansive mappings ⋮ Strong convergence of modified Ishikawa iteration for two asymptotically nonexpansive mappings and semigroups ⋮ Fixed Point Theorems for Mean Nonexpansive Mappings in CAT(0) Spaces ⋮ Fixed points of asymptotically regular semigroups in Banach spaces ⋮ Approximating a common fixed point of finite family of asymptotically quasi-nonexpansive mappings in Banach spaces ⋮ The fixed point property for multivalued nonexpansive mappings ⋮ On Banach space properties that are not invariant under the Banach-Mazur distance 1 ⋮ Some geometric properties in modular spaces and application to fixed point theory ⋮ Fixed point theorems and demiclosedness principle for mappings of asymptotically nonexpansive type in Banach spaces ⋮ A new geometrical coefficient for Banach spaces and its applications in fixed point theory ⋮ Strong convergence theorems for a countable family of Lipschitzian mappings ⋮ Strong convergence to common fixed points for countable families of asymptotically nonexpansive mappings and semigroups ⋮ The fixed point property of Orlicz sequence spaces equipped with the \(p\)-Amemiya norm ⋮ Geometrical coefficients and the structure of the fixed-point set of asymptotically regular mappings in Banach spaces ⋮ Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups ⋮ On the structure of fixed-point sets of asymptotically regular semigroups ⋮ Certain geometric structures of \(\Lambda\)-sequence spaces ⋮ Weak and strong convergence theorems of modified Ishikawa iteration for an infinitely countable family of pointwise asymptotically nonexpansive mappings in Hilbert spaces ⋮ Common fixed points approximation for asymptotically nonexpansive semigroup in Banach spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Asymptotic behavior for asymptotically nonexpansive mappings ⋮ Cloud hybrid methods for solving split equilibrium and fixed point problems for a family of countable quasi-Lipschitz mappings and applications ⋮ Fixed point theorems for (L)-type mappings in complete CAT(0) spaces ⋮ Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings ⋮ Asymptotic normal structure and the semi-opial property ⋮ Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings ⋮ Strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups ⋮ Another look at Cesàro sequence spaces ⋮ Relationships between properties that imply the weak fixed point property ⋮ Convergence theorems of common elements for equilibrium problems and fixed point problems ⋮ Existence and approximation of fixed points of nonlinear mappings in spaces with weak uniform normal structure ⋮ Does Kirk's theorem hold for multivalued nonexpansive mappings? ⋮ Fixed-point theorems for asymptotically regular mappings in Orlicz function spaces ⋮ Uniform property (K) and its related properties ⋮ Demiclosedness principle and asymptotic behavior for nonexpansive mappings in metric spaces ⋮ A note on properties that imply the fixed point property ⋮ Nearly uniformly noncreasy Banach spaces ⋮ Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups ⋮ An overview on the Prus-Szczepanik condition ⋮ On property \((M)\) and its generalizations ⋮ Generalized Projection Algorithms for Nonlinear Operators ⋮ Hybrid Mann-Halpern iteration methods for finding fixed points involving asymptotically nonexpansive mappings and semigroups ⋮ Split Variational Inclusion Problem and Fixed Point Problem for Asymptotically Nonexpansive Semigroup with Application to Optimization Problem ⋮ On strong convergence by the hybrid method for families of mappings in Hilbert spaces ⋮ Unnamed Item ⋮ Strong convergence theorems of hybrid methods for two asymptotically nonexpansive mappings in Hilbert spaces ⋮ Common fixed points of two nonexpansive mappings in Banach spaces ⋮ On strong convergence by the hybrid method for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings ⋮ Asymptotic behaviour for an almost-orbit of nonexpansive semigroups in Banach spaces ⋮ Unnamed Item ⋮ Weak uniform normal structure and fixed points of asymptotically regular semigroups ⋮ Unnamed Item ⋮ Some Fixed Point Results for Commuting Families of Mappings in Modular Spaces ⋮ Asymptotic behavior for almost-orbits of a reversible semigroup of non-Lipschitzian mappings in a metric space. ⋮ Structure of the fixed point set of asymptotically nonexpansive mappings in Banach spaces with weak uniformly normal structure ⋮ Locally uniform Opial conditions.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Iterative construction of fixed points of asymptotically nonexpansive mappings
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Normal structure coefficients for Banach spaces
• Asymptotic centers and nonexpansive mappings in conjugate Banach spaces
• Nonlinear ergodic theorems and weak convergence theorems
• Banach spaces which are nearly uniformly convex
• Some geometric properties related to the fixed point theory for nonexpansive mappings
• Approximation of Fixed Points of Asymptotically Nonexpansive Mappings
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• A Generalization of Uniformly Rotund Banach Spaces
• A Proof of the Mean Ergodic Theorem for Nonexpansive Mappings in Banach Space
• Construction of Fixed Points for Asymptotically Nonexpansive Mappings
• Existence and convergence for fixed points of mappings of asymptotically nonexpansive type
• A nonlinear ergodic theorem for asymptotically nonexpansive mappings
• Lower bounds for normal structure coefficients
• Banach spaces with the uniform opial property
• Weak Convergence to the Fixed Point of an Asymptotically Nonexpansive Map
• Fixed point theorems for asymptotically nonexpansive mappings
• Fixed Point Iteration Processes for Asymptotically Nonexpansive Mappings
• On uniform opial condition and uniform Kadec-Klee property in Banach and metric spaces
• Semicontractive and semiaccretive nonlinear mappings in Banach spaces
• Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings