An explicit iteration for asymptotic centers of orbits of nonexpansive mappings in Banach spaces

DOI10.1016/0021-9045(89)90082-8zbMath0676.41040OpenAlexW2122850974MaRDI QIDQ1122732

Norimichi Hirano, Kazuo Kido, Takahashi, Wataru

Publication date: 1989

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(89)90082-8

zbMATH Keywords

algorithmiteration schemeasymptotic center

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Cites Work

• Amenable semigroups
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Remarks on nonlinear ergodic theory
• A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space
• Some geometric properties related to the fixed point theory for nonexpansive mappings
• A Proof of the Mean Ergodic Theorem for Nonexpansive Mappings in Banach Space
• On Asymptotic Centers and Fixed Points of Nonexpansive Mappings
• A general convergence principle in nonlinear functional analysis
• A Nonlinear Ergodic Theorem for an Amenable Semigroup of Nonexpansive Mappings in a Hilbert Space
• Nonlinear ergodic theorems
• Fixed Point Theorems in Uniformly Convex Banach Spaces
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