A new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in Banach spaces

We introduce a new general system of variational inclusions in banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth banach space. furthermore,strong convergence theorems are established under some certain control conditions. as applications,finding a common solution for a system of variational inequality problems and minimization problems is given. © 2011 pongsakorn sunthrayuth and poom kumam.