A modified Mann iteration by boundary point method for finding minimum-norm fixed point of nonexpansive mappings

DOI10.1155/2013/768595zbMath1417.47020OpenAlexW1970802986WikidataQ58917419 ScholiaQ58917419MaRDI QIDQ370200

Wenlong Zhu, Songnian He

Publication date: 19 September 2013

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/768595

zbMATH Keywords

strong convergencenonexpansive mapsmodified Mann iterationboundary point methodminimum-norm fixed point

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

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• Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces
• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Approximating curve and strong convergence of the \(CQ\) algorithm for the split feasibility problem
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Geometry of Banach spaces. Selected topics
• An example concerning fixed points
• Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces
• Convergence of generalized proximal point algorithms
• Strong convergence of modified Mann iterations
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
• Viscosity approximation methods for fixed-points problems
• Strong convergence of the CQ method for fixed point iteration processes
• Construction of fixed points of nonlinear mappings in Hilbert space
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Fixed Points by a New Iteration Method
• Fixed points of nonexpanding maps
• Mean Value Methods in Iteration