The Mann algorithm in a complete geodesic space with curvature bounded above

DOI10.1186/1687-1812-2013-336zbMath1319.47054OpenAlexW2139209856WikidataQ59303007 ScholiaQ59303007MaRDI QIDQ402514

Satit Saejung, Yasunori Kimura, Pongsakorn Yotkaew

Publication date: 28 August 2014

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2013-336

zbMATH Keywords

fixed pointnonexpansive mappingquasi-nonexpansive mapping\(\Delta\)-convergenceMann algorithm\(CAT(\kappa)\) 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)

Related Items

Spherical nonspreadingness of resolvents of convex functions in geodesic spaces ⋮ CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT() SPACES ⋮ On a proximal-point algorithm for solving the minimization problem and common fixed-point problem in CAT\((k)\) spaces ⋮ Unnamed Item ⋮ Two modified proximal point algorithms in geodesic spaces with curvature bounded above ⋮ Convex feasibility problems on uniformly convex metric spaces

Cites Work

• Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one
• Convergence of subsets of a complete geodesic space with curvature bounded above
• Mann's algorithm for nonexpansive mappings in CAT\((\kappa)\) spaces
• A concept of convergence in geodesic spaces
• CAT\((k)\)-spaces, weak convergence and fixed points
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• Fixed points of uniformly Lipschitzian mappings
• Mean Value Methods in Iteration
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