VISCOSITY APPROXIMATION METHODS FOR THE FIXED-POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS

The iterative scheme of fixed point solutions to variational inequalities of nonexpansive semigroups is researched in the real Banach space with a uniformly Gateaux differentiable normin this paper. Utilizing the relationship between the variational inequalities and fixed point solution, together with the approach of viscosity approximation, we establish the two-step iterative format of fixed point concerning the nonexpansive semigroups and prove the iterative sequences obtained by this approach possess strong convergence under certain conditions and will strongly converge to the unique solution of certain variational inequality.