A hybrid iterative scheme for mixed equilibrium problems and fixed point problems

Authors:
Lu-Chuan Ceng;Jen-Chih Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
Cited 20

Equilibrium programming using proximal-like algorithms

Mathematical Programming: Series A and B
Interative schemes for solving mixed variational-like inequalites1,2

Journal of Optimization Theory and Applications
Descent methods for equilibriumproblems in a Banach space

Computers & Mathematics with Applications
Convergence theorems for nonexpansive mappings and feasibility problems

Mathematical and Computer Modelling: An International Journal

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

Journal of Computational and Applied Mathematics
Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces

Journal of Computational and Applied Mathematics
Two extragradient methods for generalized mixed equilibrium problems, nonexpansive mappings and monotone mappings

Computers & Mathematics with Applications
A hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k-strict pseudo-contractions

Journal of Computational and Applied Mathematics
Strong convergence theorems for solving equilibrium problems and fixed point problems of ξ-strict pseudo-contraction mappings by two hybrid projection methods

Journal of Computational and Applied Mathematics
Strong convergence of shrinking projection methods for quasi-φ-nonexpansive mappings and equilibrium problems

Journal of Computational and Applied Mathematics
Iterative algorithms for a general system of generalized nonlinear mixed composite-type equilibria

Computers & Mathematics with Applications
Minimization of equilibrium problems, variational inequality problems and fixed point problems

Journal of Global Optimization
A modified Halpern-type iteration algorithm for a family of hemi-relatively nonexpansive mappings and systems of equilibrium problems in Banach spaces

Journal of Computational and Applied Mathematics
Algorithms for approximating minimization problems in Hilbert spaces

Journal of Computational and Applied Mathematics
Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

Computers & Mathematics with Applications
Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems

Computers & Mathematics with Applications
Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems

Mathematical and Computer Modelling: An International Journal
Strong convergence theorems for a general system of variational inequality problems, mixed equilibrium problems and fixed points problems with applications

Mathematical and Computer Modelling: An International Journal
Strong convergence theorems for fixed point problems, variational inequality problems and system of generalized mixed equilibrium problems

Mathematical and Computer Modelling: An International Journal
Hybrid extragradient-like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems

Journal of Global Optimization
Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces

Journal of Global Optimization
Strong and weak convergence theorems for general mixed equilibrium problems and variational inequality problems and fixed point problems in Hilbert spaces

Journal of Computational and Applied Mathematics
An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems

Journal of Global Optimization
On general systems of variational inequalities

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.30

Visualization

Abstract

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem (MEP) and the set of common fixed points of finitely many nonexpansive mappings in a real Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the MEP. Second, by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings. Furthermore, we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings.