Title :
Hybrid algorithm for maximal monotone operators, quasi-ϕ-nonexpansive mappings and equilibrium problems in banach spaces
Author :
Fan, Shu-xin ; Duan, Li-ling ; Li, Wei
Author_Institution :
Sch. of Math. & Stat., Hebei Univ. of Econ. & Bus., Shijiazhuang, China
Abstract :
In this paper, some hybrid iterative algorithms for approximating the common element of the set of solutions of an equilibrium problem, the set of common fixed points of finitely many quasi-φ-nonexpansive mappings and the set of common zeroes of finitely many maximal monotone operators in a uniformly smooth and uniformly convex Banach space are presented. Some strong convergence theorems are obtained which extend and complement the previous results. Moreover, the applications of the iterative algorithms to optimization problem and minimizer problem are demonstrated. The work done in this paper has significance in the area of economic mathematics, engineering sciences and some others.
Keywords :
Banach spaces; convergence; iterative methods; mathematical operators; minimisation; Banach spaces; common zeroes; convergence theorem; economic mathematics; engineering sciences; equilibrium problem; finitely many maximal monotone operators; finitely many quasi-φ-nonexpansive mapping; hybrid iterative algorithm; minimizer problem; optimization problem; uniformly convex Banach space; uniformly smooth Banach space; Approximation algorithms; Cybernetics; Economics; Iterative methods; Machine learning; Machine learning algorithms; Equilibrium problem; Hybrid algorithm; Maximal monotone operator; Quasi-ϕ-nonexpansive mapping;
Conference_Titel :
Machine Learning and Cybernetics (ICMLC), 2011 International Conference on
Print_ISBN :
978-1-4577-0305-8
DOI :
10.1109/ICMLC.2011.6016826
