Weak and strong convergence theorems of three step iteration process with errors for nonself-asymptotically nonexpansive mappings

DOI10.1016/j.mcm.2010.05.006zbMath1202.65069OpenAlexW1965717937MaRDI QIDQ614306

Xiangsheng Xie, Li-Ping Yang

Publication date: 27 December 2010

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2010.05.006

zbMATH Keywords

common fixed pointKadec-Klee propertynonself-asymptotically nonexpansive mappingsthree step iteration

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Strong convergence theorems for a countable family of totally quasi-\(\phi\)-asymptotically nonexpansive nonself mappings in Banach spaces with applications ⋮ Strong convergence theorems for a countable family of quasi-\(\phi \)-asymptotically nonexpansive nonself mappings ⋮ Convergence theorems for common fixed points of nonself asymptotically nonextensive mappings ⋮ Strong convergence theorems for solutions of equilibrium problems and common fixed points of a finite family of asymptotically nonextensive nonself mappings ⋮ Strong convergence theorems for a countable family of total quasi-\(\phi\)-asymptotically nonexpansive nonself mappings ⋮ Strong convergence theorems of the Halpern-Mann's mixed iteration for a totally quasi-\(\phi\)-asymptotically nonexpansive nonself multi-valued mapping in Banach spaces

Cites Work

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• Weak and strong convergence of a scheme with errors for two nonexpansive mappings
• Strong convergence of averaging iterations of nonexpansive nonself-mappings
• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Convergence analysis and applications of the Glowinski-Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• New approximation schemes for general variational inequalities
• Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings
• Approximating fixed points of non-self nonexpansive mappings in Banach spaces
• Strong and weak convergence theorems for asymptotically nonexpansive mappings.
• A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Approximating Fixed Points of Nonexpansive Mappings
• Strong convergence of approximants to fixed points of nonexpansive nonself-mappings in Banach spaces
• Strong convergence theorems for nonexpansive nonself-mappings in Banach spaces
• Nonexpansive retracts of Banach spaces
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings