Strong convergence theorems for a generalized equilibrium problem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a Hilbert space

DOI10.1155/2010/230304zbMath1204.47088OpenAlexW2165026113WikidataQ59253654 ScholiaQ59253654MaRDI QIDQ1958026

Giuseppe Marino, Fuhai Wang, Sheng-Hua Wang

Publication date: 28 September 2010

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

Full work available at URL: https://eudml.org/doc/227092

zbMATH Keywords

strong convergencegeneralized equilibrium problemnonexpansive mappings in a Hilbert spacerelaxed monotone mapping

Mathematics Subject Classification ID

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

Related Items

Some existence and convergence theorems for solving a system of hierarchical optimization problems ⋮ Strong convergence theorems for equilibrium problems and asymptotically quasi-\(\phi\)-nonexpansive mappings in the intermediate sense ⋮ Convergence theorems for Bregman \(K\)-mappings and mixed equilibrium problems in reflexive Banach spaces ⋮ Existence and iterative approximation methods for generalized mixed vector equilibrium problems with relaxed monotone mappings ⋮ Composite algorithms for minimization over the solutions of equilibrium problems and fixed point problems ⋮ Strong convergence of a new iterative method for infinite family of generalized equilibrium and fixed-point problems of nonexpansive mappings in Hilbert spaces ⋮ An implicit extragradient method for hierarchical variational inequalities ⋮ Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications ⋮ Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansive mappings ⋮ Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces ⋮ A general composite algorithm for solving general equilibrium problems and fixed point problems in Hilbert spaces ⋮ New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces ⋮ Split common fixed point problems for demicontractive operators

Cites Work

• Unnamed Item
• Unnamed Item
• Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces
• Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space
• Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem
• Viscosity approximation methods for equilibrium problems and fixed point problems of nonexpansive mappings and inverse-strongly monotone mappings
• Nonlinear variational inequalities on convex subsets of Banach spaces
• Variational-like inequalities with generalized monotone mappings in Banach spaces
• Weak convergence theorems for nonexpansive mappings and monotone mappings
• Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings
• A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings
• Construction of fixed points of nonlinear mappings in Hilbert space
• On nonlinear variational inequalities