Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces

摘要

We consider the variational inequality problem for afamily of operators of a nonempty closed convex subset of a 2-uniformly convex Banach space with a uniformly Gâteaux differentiable norm, into its dual space. We assume some properties for the operators and get strong convergence to a common solution to the variational inequality problem by the hybridmethod proposed by Haugazeau. Using these results, we obtain several resultsfor the variational inequality problem and the proximal point algorithm.