Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces

DOI10.1016/0362-546X(88)90059-4zbMath0679.47031OpenAlexW2034451066MaRDI QIDQ4728874

Kazuo Kido, Norimichi Hirano, Takahashi, Wataru

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0362-546x(88)90059-4

zbMATH Keywords

nonexpansive retractionsnonlinear ergodic theorems for commutative semigroups of nonexpansive mappings without using compact means

Mathematics Subject Classification ID

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

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Cites Work

• Unnamed Item
• Unnamed Item
• Amenable semigroups
• Nonlinear ergodic theorems for an amenable semigroup of nonexpansive mappings in a Banach space
• A note on a mean ergodic theorem for nonlinear semigroups
• Weak convergence and nonlinear ergodic theorems for reversible semigroup of nonexpansive mappings
• Means on commutative semigroups and nonlinear ergodic theorems
• The existence of nonexpansive retractions in Banach spaces
• Fixed point theorems for families of nonexpansive mappings on unbounded sets
• Mean ergodic theorems for semigroups of linear operators
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space
• Almost convergence and nonlinear ergodic theorems
• A contribution to the theory of divergent sequences
• Asymptotic behavior of commutative semigroups of nonexpansive mappings in Banach spaces
• 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
• Invariant functions for amenable semigroups of positive contractions on $L^{1}$

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