Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces

DOI10.1016/j.jmaa.2004.08.022zbMath1062.47069OpenAlexW2063298310MaRDI QIDQ1763815

Jong Soo Jung

Publication date: 22 February 2005

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.2004.08.022

zbMATH Keywords

duality mappingnonexpansive mappingiteration schemesmooth normcommon fixed pointssunny and nonexpansive retractionuniformly smooth normweak sequential continuity

Mathematics Subject Classification ID

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

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Cites Work

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• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Geometry of Banach spaces. Selected topics
• Strong convergence to common fixed points of families of nonexpansive mappings
• Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces.
• An iterative approach to quadratic optimization
• The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• A characterization of strict convexity of Banach spaces and other uses of duality mappings
• Some geometric properties related to the fixed point theory for nonexpansive mappings
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings
• Quadratic optimization of fixed points of nonexpansive mappings in hubert space
• Positivity of duality mappings
• Fixed points of nonexpanding maps
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• The Mann process for perturbed \(m\)-accretive operators in Banach spaces

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