Strong convergence of a general iteration scheme in \(CAT(0)\) spaces

DOI10.1016/j.na.2010.09.029zbMath1202.47076OpenAlexW2029400720MaRDI QIDQ611186

Hafiz Fukhar-ud-din, Abdul Rahim Khan, Mohamed Amine Khamsi

Publication date: 14 December 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.09.029

zbMATH Keywords

iteration schemecommon fixed pointconvex metric spacesemi-compactness\(CAT(0)\) spaceasymptotically (quasi-)nonexpansive mapcondition (AV)

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

Existence and higher arity iteration for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces ⋮ Kirk type iteration process and convex feasibility problem in CAT(0) space ⋮ Convergence of a general algorithm of asymptotically nonexpansive maps in uniformly convex hyperbolic spaces ⋮ Existence and convergence theorems of fixed points for multi-valued SCC-, SKC-, KSC-, SCS- and C-type mappings in hyperbolic spaces ⋮ On the Ishikawa iteration processes for multivalued mappings in some \(\mathrm{CAT}(\kappa)\) spaces ⋮ Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space ⋮ On an open problem of Kyung Soo Kim ⋮ \(\Delta\)-convergence theorems for multi-valued nonexpansive mappings in hyperbolic spaces ⋮ Common fixed point iterations of non-Lipschitzian mappings in a convex metric space ⋮ Generalized hybrid mappings on CAT(\(\kappa\)) spaces ⋮ An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces ⋮ Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces ⋮ Convergence of three-step iterations for Ciric-quasi contractive operator in \(\mathbf{CAT(0)}\) spaces ⋮ \(S\)-iteration process for quasi-contractive mappings ⋮ On the strong convergence of a modified S-iteration process for asymptotically quasi-nonexpansive mappings in a CAT(0) space ⋮ Convergence analysis of a general iteration schema of nonlinear mappings in hyperbolic spaces ⋮ Mixed type iteration for total asymptotically nonexpansive mappings in hyperbolic spaces ⋮ About fixed points in \(\mathrm{CAT}(0)\) spaces under a combined structure of two self-mappings ⋮ Strong convergence of an implicit algorithm in CAT(0) spaces ⋮ Strong convergence of modified Halpern iterations in \(\mathrm{CAT}(0)\) spaces ⋮ Common fixed points for asymptotic pointwise nonexpansive mappings in metric and Banach spaces ⋮ Convergence theorems for nonexpansive semigroups in spaces ⋮ Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces ⋮ Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces ⋮ Viscosity Iteration in CAT(κ) Spaces ⋮ Fixed point iterations for Prešić-Kannan nonexpansive mappings in product convex metric spaces ⋮ Ishikawa iteration process for asymptotic pointwise nonexpansive mappings in metric spaces ⋮ Strong and \(\delta\)-convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces ⋮ Fixed point theorems for \(N\)-generalized hybrid mappings in uniformly convex metric spaces ⋮ Approximating common fixed points in hyperbolic spaces ⋮ A generalization of Suzuki's Lemma ⋮ Implicit Ishikawa approximation methods for nonexpansive semigroups in CAT(0) spaces ⋮ Convergence analysis of a multi-step iteration for a finite family of asymptotically quasi-nonexpansive mappings ⋮ Strong and \(\triangle\)-convergence theorems for two asymptotically nonexpansive mappings in the intermediate sense in \(\operatorname{CAT}(0)\) spaces ⋮ Approximation of common fixed point of two quasi-nonexpansive mappings in convex metric spaces ⋮ Unnamed Item ⋮ Common fixed point of generalized asymptotic pointwise (quasi-) nonexpansive mappings in hyperbolic spaces ⋮ Unnamed Item ⋮ Strong and \(\triangle\)-convergence of Moudafi's iterative algorithm for generalized nonexpansive mappings in convex metric spaces ⋮ Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces ⋮ Convergence of modified \(S\)-iteration process for two asymptotically quasi-nonexpansive type mappings in CAT(0) spaces ⋮ Convergence of modified \(S\)-iteration process for two asymptotically nonexpansive mappings in the intermediate sense in CAT(0) spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Iterative construction of fixed points of asymptotically nonexpansive mappings
• A quadratic rate of asymptotic regularity for CAT(0)-spaces
• Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications
• Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces
• Common fixed points of nonexpansive mappings by iteration
• Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces
• Iteration processes for nonlinear mappings in convex metric spaces
• Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces
• Reductive groups over a local field
• Fixed point theorems in CAT(0) spaces and \(\mathbb R\)-trees
• On uniformly Lipschitzian multivalued mappings in Banach and metric spaces
• Approximating common fixed points of asymptotically quasi-nonexpansive mappings by a \(k+1\)-step iterative scheme with error terms
• A convexity in metric space and nonexpansive mappings. I.
• Fixed point and selection theorems in hyperconvex spaces
• An Introduction to Metric Spaces and Fixed Point Theory
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Iterative sequences for asymptotically quasi-nonexpansive mappings.

This page was built for publication: Strong convergence of a general iteration scheme in \(CAT(0)\) spaces