Title :
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
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;
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
DOI :
10.1109/ICMLC.2009.5212247
