An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

DOI10.2478/s11533-009-0003-xzbMath1195.49017OpenAlexW1971286683MaRDI QIDQ1040209

Jen-Chih Yao, Adrian Petruşel

Publication date: 24 November 2009

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-009-0003-x

zbMATH Keywords

variational inequalitiesfixed pointnonexpansive mappingviscosity approximation methodmodified extragradient method\(\alpha \)-inverse-strongly-monotone mapping

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Fixed-point theorems (47H10) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items

Two algorithms for solving single-valued variational inequalities and fixed point problems ⋮ Retraction algorithms for solving variational inequalities, pseudomonotone equilibrium problems, and fixed-point problems in Banach spaces ⋮ Extragradient-type method for optimal control problem with linear constraints and convex objective function ⋮ Extragradient methods and linesearch algorithms for solving Ky Fan inequalities and fixed point problems ⋮ Strong convergence theorems for variational inequalities and fixed point problems of asymptotically strict pseudocontractive mappings in the intermediate sense ⋮ On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space ⋮ A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of hybrid steepest-descent methods for variational inequalities
• Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems
• A general iterative scheme for nonexpansive mappings and inverse-strongly monotone mappings
• Viscosity approximation methods for nonexpansive mappings and inverse-strongly monotone mappings in Hilbert spaces
• Viscosity approximation methods for nonexpansive mappings and monotone mappings
• Regularization of nonlinear ill-posed variational inequalities and convergence rates
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Modified projection method for pseudomonotone variational inequalities
• Viscosity approximation methods for nonexpansive mappings
• Viscosity approximation methods for fixed-points problems
• Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings
• Construction of fixed points of nonlinear mappings in Hilbert space
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• On the Maximality of Sums of Nonlinear Monotone Operators

This page was built for publication: An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems