Asymptotically strict pseudocontractive mappings in the intermediate sense

DOI10.1016/j.na.2008.07.007zbMath1221.47122OpenAlexW1969798592MaRDI QIDQ1012063

Hong-Kun Xu, Jen-Chih Yao, Daya Ram Sahu

Publication date: 14 April 2009

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/j.na.2008.07.007

zbMATH Keywords

strong convergenceweak convergenceasymptotically nonexpansive mappingmetric projectiondemiclosedness principleasymptotically strict pseudocontractive mapping

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Weak and strong convergence of a scheme with errors for two nonexpansive mappings
• Iterative construction of fixed points of asymptotically nonexpansive mappings
• Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings
• Approximation of common fixed points for finite families of nonself asymptotically nonexpansive mappings in Banach spaces
• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Fixed point iterations for certain nonlinear mappings
• Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces
• Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces
• A new iterative approximation of fixed points for asymptotically contractive type mappings in Banach spaces
• Strong and weak convergence theorems for asymptotically nonexpansive mappings.
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions
• Strong convergence of the CQ method for fixed point iteration processes
• Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
• Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings
• Weak and strong convergence for fixed points of asymptotically non-expansive mappings
• Convergence Theorems for Mappings Which Are Asymptotically Nonexpansive in the Intermediate Sense
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Existence and convergence for fixed points of mappings of asymptotically nonexpansive type
• The Nonlinear Ergodic Theorem for Asymptotically Nonexpansive Mappings in Banach Spaces
• Fixed Point Iteration Processes for Asymptotically Nonexpansive Mappings
• Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings