Implicit Iterations of Two Finite Families for Nonexpansive Mappings in Banach Spaces

DOI10.1080/01630560701348525zbMath1122.47054OpenAlexW2019195161MaRDI QIDQ5297958

Kasamsuk Ungchittrakool, Somyot Plubtieng, Rabian Wangkeeree

Publication date: 16 July 2007

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560701348525

zbMATH Keywords

fixed pointsstrong convergenceweak convergenceOpial conditionnonexpansive mapsimplicit iterationKadec-Klee propertycondition (B)finite familysemicompactness

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)

Related Items (9)

An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings ⋮ An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces ⋮ Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces ⋮ Weak and Strong Convergence of an Implicit Iteration Process in Uniformly Convex Banach Spaces ⋮ Composite Implicit Iteration Process for Two Finite Families of Generalized Asymptotically Quasi-Nonexpansive Mappings ⋮ Weak and strong convergence theorems for a finite family of non-Lipschitzian nonself mappings in Banach spaces ⋮ On the implicit iterative process for strictly pseudo-contractive mappings in Banach spaces ⋮ Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings ⋮ An Implicit Iteration for a Countable Family of Nonexpansive Mappings in Banach Spaces

Cites Work

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• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Fixed point iterations for certain nonlinear mappings
• Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups
• Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings
• AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Nonlinear ergodic theorems for commutative semigroups of asymptotically 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
• Strong convergence theorems for nonexpansive nonself-mappings
• CONVERGENCE OF IMPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• Weak convergence of the sequence of successive approximations for nonexpansive mappings

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