Strong convergence of the composite Halpern iteration

DOI10.1016/J.JMAA.2007.07.062zbMath1135.47052OpenAlexW1999444271MaRDI QIDQ2465859

Xiaolong Qin, Meijuan Shang, Yongfu Su

Publication date: 10 January 2008

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.07.062

zbMATH Keywords

fixed pointnonexpansive mappingBanach spacenonexpansive retractionconvergence theoremsunny retraction3-step fixed point iterative method

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (8)

Strong convergence of a multiple-step iterative process for nonexpansive mappings ⋮ Steepest-descent Ishikawa iterative methods for a class of variational inequalities in Banach spaces ⋮ Modified Halpern's iteration for fixed point theory of a finite family of \(G\)-nonexpansive mappings endowed with graph ⋮ COMMON FIXED POINTS OF A PAIR OF NON-EXPANSIVE MAPPINGS WITH APPLICATIONS TO CONVEX FEASIBILITY PROBLEMS ⋮ Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces ⋮ Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings ⋮ Convergence theorems of common fixed points for a family of Lipschitz quasi-pseudocontractions ⋮ Strong convergence of viscosity iteration methods for nonexpansive mappings

Cites Work

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• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• An iterative approach to quadratic optimization
• Strong convergence of modified Mann iterations
• Nonexpansive projections on subsets of Banach spaces
• Asymptotic behavior of contractions in Banach spaces
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• Iterative Algorithms for Nonlinear Operators
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE
• Fixed points of nonexpanding maps

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