VARIATIONAL INEQUALITIES GOVERNED BY BOUNDEDLY LIPSCHITZIAN AND STRONGLY MONOTONE OPERATORS

Consider the variational inequality VI(C, F) of finding a point x* is an element of C satisfying the property < Fx*, x - x*> >= 0 for all x is an element of C, where C is a nonempty closed convex subset of a real Hilbert space H and F : C -> H is a nonlinear mapping. If F is boundedly Lipschitzian and strongly monotone, then we prove that VI(C, F) has a unique solution and iterative algorithms can be devised to approximate this solution. In the case where C is the set of fixed points of a nonexpansie mapping, we also invent a hybrid iterative algorithm to approximate the unique solution of VI(C, F).