Asymptotic behavior of commutative semigroups of nonexpansive mappings in Banach spaces

DOI10.1016/0362-546X(86)90002-7zbMath0594.47053MaRDI QIDQ3725048

Takahashi, Wataru, Norimichi Hirano, Kazuo Kido

Publication date: 1986

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

zbMATH Keywords

Cesàro meanscontraction semigroupnonexpansive mappingsFréchet differentiable normnonlinear mean ergodic theorem for commutative semigroups ofnonlinear mean ergodic theorem for commutative semigroups of nonexpansive mappings

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces ⋮ Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings ⋮ Strong ergodic theorem for commutative semigroup of non-Lipschitzian mappings in multi-Banach space ⋮ Asymptotically invariant net and fixed point set for semigroup of nonexpansive mappings ⋮ Strong convergence and nonlinear ergodic theorems for commutative semigroups of nonexpansive mappings ⋮ Convergence of approximated sequences for nonexpansive mappings ⋮ Nonlinear Ergodic Theorem for Positively Homogeneous Nonexpansive Mappings in Banach Spaces ⋮ Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces ⋮ A mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense ⋮ Weak convergence theorems for asymptotically nonexpansive mappings and semigroups ⋮ Means on commutative semigroups and nonlinear ergodic theorems

Cites Work

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• On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak \(\omega\)-limit set
• Une méthode itérative de résolution d'une inéquation variationnelle
• Remarks on nonlinear ergodic theory
• Nonlinear ergodic theorems for nonexpansive mappings in Hilbert spaces
• A note on segmenting Mann iterates
• A contribution to the theory of divergent sequences
• A Proof of the Mean Ergodic Theorem for Nonexpansive Mappings in Banach Space
• A Nonlinear Ergodic Theorem for an Amenable Semigroup of Nonexpansive Mappings in a Hilbert Space
• Nonlinear evolution equations and nonlinear ergodic theorems
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• Applications of the Hahn-Banach Theorem in Approximation Theory
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