Strong convergence to a solution of a variational inequality problem in Banach spaces

We consider the variational inequality problem for a family 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 hybrid method proposed by haugazeau. using these results,we obtain several results for the variational inequality problem and the proximal point algorithm. © 2014 yasunori kimura and kazuhide nakajo.