Hybrid viscosity approximation methods for general systems of variational inequalities in Banach spaces

Fixexd point theory and applications

Abdul Latif¹  Abdullah E Al-Mazrooei¹  Jen C Yao¹  Buthinah ABin Dehaish¹ 

[1] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: general system of variational inequalities;    iterative methods;    nonexpansive mapping;    sunny nonexpansive retraction;    fixed point;    weakly sequentially continuous duality map;    uniform smoothness;   

DOI  :  10.1186/1687-1812-2013-258

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Let X be a uniformly convex and 2-uniformly smooth Banach space. In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (in short, GSVI) in X based on Korpelevich’s extragradient method and viscosity approximation method. We show that the proposed algorithms converge strongly to some solutions of the GSVI under consideration. When X is a 2-uniformly smooth Banach space with weakly sequentially continuous duality mapping, we also propose two methods, which were inspired and motivated by Korpelevich’s extragradient method and Mann’s iterative method. Furthermore, it is also proven that the proposed algorithms converge strongly to some solutions of the considered GSVI. MSC:49J30, 47H09, 47J20.

【 授权许可】

CC BY