Halpern type iteration with multiple anchor points in a Hadamard space

DOI10.1186/S13660-015-0693-5zbMath1338.47098OpenAlexW2167396445WikidataQ59404185 ScholiaQ59404185MaRDI QIDQ264516

Hideyuki Wada, Yasunori Kimura

Publication date: 31 March 2016

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

Full work available at URL: https://doi.org/10.1186/s13660-015-0693-5

zbMATH Keywords

fixed pointnonexpansive mapping\(\operatorname{CAT}(0)\) spaceapproximation theoremgeodesic space

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Cites Work

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• Mann's algorithm for nonexpansive mappings in CAT\((\kappa)\) spaces
• A concept of convergence in geodesic spaces
• Halpern's iteration in CAT(0) spaces
• Approximation of fixed points of nonexpansive mappings
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• Existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in Banach spaces
• Strong convergence to common fixed points of families of nonexpansive mappings
• An iterative approach to quadratic optimization
• Convergence to common fixed points of a finite family of nonexpansive mappings
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space

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