A hybrid method for mixed equilibrium problems and fixed points problems

Author

Zhang, Li Juan ; Song, Hong-ying

Author_Institution

Coll. of Math. & Comput., Hebei Univ., Baoding, China

Volume

3

fYear

2009

fDate

12-15 July 2009

Firstpage

1647

Lastpage

1652

Abstract

In this paper, we introduce a iterative scheme by a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of common fixed points of finitely many nonexpansive mappings in a Hilbert space. We prove a strong convergence theorem for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization.The results extended and improved the corresponding results of L.C. Ceng, J.C. Yao and others.

Keywords

Hilbert spaces; convergence of numerical methods; iterative methods; minimisation; set theory; Hilbert space; convergence theorem; fixed points problem; hybrid iterative method; minimization; mixed equilibrium problem; nonexpansive mapping; optimality condition; solution set; variational inequality; Cybernetics; Machine learning; Fixed point; Hybrid iterative scheme; Minimization problem; Mixed equilibrium problems; Nonexpansive mapping; inverse-strongly;

fLanguage

English

Publisher

ieee

Conference_Titel

Machine Learning and Cybernetics, 2009 International Conference on

Conference_Location

Baoding

Print_ISBN

978-1-4244-3702-3

Electronic_ISBN

978-1-4244-3703-0

Type

conf

DOI

10.1109/ICMLC.2009.5212247

Filename

5212247