Strong convergence of viscosity approximation methods for nonexpansive mappings in \(\text{CAT}(0)\) spaces

DOI10.1155/2012/421050zbMath1281.47059OpenAlexW1976650207WikidataQ58906896 ScholiaQ58906896MaRDI QIDQ442923

Luo Yi Shi, Ru Dong Chen

Publication date: 6 August 2012

Published in: Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/421050

zbMATH Keywords

strong convergence\(\text{CAT}(0)\) spacesnonexpansive mappingsiteration processviscosity approximation methods

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

Viscosity approximation methods for multivalued nonexpansive mappings in geodesic spaces ⋮ Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces ⋮ \(\Delta\)-convergence problems for asymptotically nonexpansive mappings in CAT(0) spaces ⋮ A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space ⋮ An affirmative answer to Panyanak and Suantai's open question on the viscosity approximation methods for a nonexpansive multi-valued mapping in CAT(0) spaces ⋮ Successive approximations for common fixed points of a family of \(\alpha \)-nonexpansive mappings ⋮ Viscosity approximation methods for hierarchical optimization problems in \(\mathrm{CAT}(0)\) spaces ⋮ Viscosity approximation methods for asymptotically nonexpansive mapping in CAT(0) spaces ⋮ Unnamed Item ⋮ Strong convergence of new two-step viscosity iterative approximation methods for set-valued nonexpansive mappings in \(\mathrm{CAT}(0)\) spaces ⋮ General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete \(\operatorname{CAT}(0)\) spaces ⋮ Viscosity iteration method in CAT(0) spaces without the nice projection property

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A quadratic rate of asymptotic regularity for CAT(0)-spaces
• A concept of convergence in geodesic spaces
• CAT\((k)\)-spaces, weak convergence and fixed points
• Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces
• Invariant approximations in CAT(0) spaces
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces
• A note on fixed point sets in CAT(0) spaces
• Fixed point sets of parabolic isometries of CAT(0)-spaces
• Fixed points of uniformly Lipschitzian mappings
• Fixed point theorems in CAT(0) spaces and \(\mathbb R\)-trees
• Lim's theorems for multivalued mappings in CAT(0) spaces
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

This page was built for publication: Strong convergence of viscosity approximation methods for nonexpansive mappings in \(\text{CAT}(0)\) spaces