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

作者：Latif Abdul^*; Al Mazrooei Abdullah E; Bin Dehaish Buthinah A; Yao Jen C

来源：Fixed Point Theory and Applications, 2013, 2013(1): 258.

DOI：10.1186/1687-1812-2013-258

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

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%26apos;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%26apos;s extragradient method and Mann%26apos;s iterative method. Furthermore, it is also proven that the proposed algorithms converge strongly to some solutions of the considered GSVI.

• 出版日期2013-11-7