Ergodic theorems for nonexpansive curves defined on general semigroups in a Hilbert space

DOI10.1016/S0362-546X(99)00296-5zbMath0999.47049OpenAlexW2075045789MaRDI QIDQ5935779

Behzad Djafari Rouhani

Publication date: 2001

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(99)00296-5

zbMATH Keywords

ergodic theoremsalmost nonexpansive sequencesasymptotically invariant meannonexpansive curvequasi-autonomous dissipative systemsreversibilitysemi-topological semigroup

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items

Asymptotic behavior of uniformly asymptotically almost nonexpansive curves in a Hilbert space ⋮ A quantitative nonlinear strong ergodic theorem for Hilbert spaces ⋮ A note on the weak convergence of nonexpansive curves in a Hilbert space ⋮ Asymptotic behavior for almost-orbits of a reversible semigroup of non-Lipschitzian mappings in a metric space.

Cites Work

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• Asymptotic behaviour of almost nonexpansive sequences in a Hilbert space
• Nonlinear ergodic theorems for an amenable semigroup of nonexpansive mappings in a Banach space
• Asymptotic behaviour of quasi-autonomous dissipative systems in Hilbert spaces
• Weak convergence and nonlinear ergodic theorems for reversible semigroup of nonexpansive mappings
• Semigroup of nonexpansive mappings on a Hilbert space
• 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
• On the asymptotic behavior of iterates of nonexpansive mappings in Hilbert space
• On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak \(\omega\)-limit set
• On the asymptotic behavior of semigroups of nonlinear contractions in Hilbert space
• Remarks on nonlinear ergodic theory
• Nonlinear ergodic theorems for nonexpansive mappings in Hilbert spaces
• Almost convergence and nonlinear ergodic theorems
• On the existence of fixed points and ergodic retractions for Lipschitzian semigroups in Hilbert 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
• Asymptotically invariant net and fixed point set for semigroup of nonexpansive mappings
• Nonexpansive retractions and nonlinear ergodic theorems in Banach spaces
• Nonlinear ergodic theorems for semigroups of nonexpansive mappings and left ideals
• On left amenable semigroups which admit countable left invariant means
• The construction of an asymptotic center with a fixed-point property