An ergodic theorem for nonlinear semigroups of Lipschitzian mappings in Banach spaces

DOI10.1016/0362-546X(92)90052-GzbMath0782.47058MaRDI QIDQ4695748

Kok-Keong Tan, Hong-Kun Xu

Publication date: 29 June 1993

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

zbMATH Keywords

nonlinear ergodic theoremsemigroups of nonlinear operatorsasymptotically nonexpansive semigroupBanach space with Fréchet differentiable norm

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) One-parameter semigroups and linear evolution equations (47D06)

Related Items (11)

Advancements in fixed point theory in modular function spaces ⋮ On the set of common fixed points of semigroups of nonlinear mappings in modular function spaces ⋮ Strong asymptotic behavior of almost-orbits of nonlinear semigroups ⋮ Ergodic retraction theorem and weak convergence theorem for reversible semigroups of non-Lipschitzian mappings ⋮ Fixed point of asymptotic pointwise nonexpansive semigroups in metric spaces ⋮ Common fixed points for pointwise Lipschitzian semigroups in modular function spaces ⋮ Approximating common fixed points of an evolution family on a metric space via Mann iteration ⋮ COMMON FIXED POINTS FOR SEMIGROUPS OF POINTWISE LIPSCHITZIAN MAPPINGS 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 ⋮ Approximating common fixed points of semigroups in metric spaces

Cites Work

• A note on a mean ergodic theorem for nonlinear semigroups
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces
• Nonlinear ergodic theorems for nonexpansive mappings in Hilbert spaces
• Almost convergence and nonlinear ergodic theorems
• Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type
• A contribution to the theory of divergent sequences
• A Proof of the Mean Ergodic Theorem for Nonexpansive Mappings in Banach Space
• The Nonlinear Ergodic Theorem for Asymptotically Nonexpansive Mappings in Banach Spaces
• Nonlinear evolution equations and nonlinear ergodic theorems
• Semicontractive and semiaccretive nonlinear mappings in Banach spaces
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
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