Nonlinear ergodic theorems for asymptotically nonexpansive mappings in Banach spaces satisfying Opial's condition

DOI10.1016/0022-247X(91)90343-XzbMath0756.47037MaRDI QIDQ1189683

Jarosław Górnicki

Publication date: 27 September 1992

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

asymptotically nonexpansive mappingOpial's conditionLipschitz normmean ergodic theorem of Baillon

Mathematics Subject Classification ID

Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Strong and weak convergence theorems for asymptotically nonexpansive mappings. ⋮ Convergence Theorems for Mappings Which Are Asymptotically Nonexpansive in the Intermediate Sense ⋮ Convergence theorems for asymptotically pseudocontractive mappings ⋮ Iterative approximation for generalized asymptotically $k$-strict pseudocontractive type mappings ⋮ A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings ⋮ Approximating fixed points of total asymptotically nonexpansive mappings ⋮ Iterative approximation of fixed points of (asymptotically) nonexpansive mappings ⋮ A note on approximating fixed points of nonexpansive mappings by the Ishikawa iteration process ⋮ Unnamed Item ⋮ Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

Cites Work

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• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Nonlinear ergodic theorems and weak convergence theorems
• A fixed point theorem for asymptotically nonexpansive mappings
• Remarks on nonlinear ergodic theory
• Nonlinear ergodic theorems for nonexpansive mappings in Hilbert spaces
• Some geometric properties related to the fixed point theory for nonexpansive mappings
• Asymptotic behavior of nonexpansive mappings
• Spazi di Opial, centri asintotici e punti fissi
• Weak Convergence to the Fixed Point of an Asymptotically Nonexpansive Map
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings

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