Convergence and certain control conditions for hybrid viscosity approximation methods

DOI10.1016/j.na.2010.05.036zbMath1229.47106OpenAlexW2017595142MaRDI QIDQ988858

Jen-Chih Yao, Lu-Chuan Ceng

Publication date: 19 August 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.2010.05.036

zbMATH Keywords

weak convergencefixed pointnonexpansive mappingHilbert spaceuniformly smooth Banach spacehybrid viscosity approximation method

Mathematics Subject Classification ID

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

Related Items

Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications ⋮ System of variational inequalities and an accretive operator in Banach spaces ⋮ An iterative method for solving a system of mixed equilibrium problems, system of quasivariational inclusions, and fixed point problems of nonexpansive semigroups with application to optimization problems ⋮ Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems ⋮ Hybrid and relaxed Mann iterations for general systems of variational inequalities and nonexpansive mappings

Cites Work

• Convergence of hybrid steepest-descent methods for variational inequalities
• Robustness of Mann type algorithm with perturbed mapping for nonexpansive mappings in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• An example concerning fixed points
• A note on approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals
• Strong convergence of modified Mann iterations
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Viscosity approximation methods for nonexpansive mappings
• Strong convergence theorems for strictly pseudocontractive mappings of Browder--Petryshyn type
• Strong convergence and certain control conditions for modified Mann iteration
• Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings
• Three-step iterative convergence theorems with errors in Banach spaces
• Strong convergence theorems of Ishikawa iteration process with errors for fixed points of Lipschitz continuous mappings in Banach spaces
• Construction of fixed points of nonlinear mappings in Hilbert space
• Equivalent Norms and the Fixed Point Property for Nonexpansive Mappings
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• A unified treatment of some iterative algorithms in signal processing and image reconstruction
• Fixed points of nonexpanding maps
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Convergence and certain control conditions for hybrid viscosity approximation methods