A new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in Banach spaces (Q554987)

Summary: 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 points of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is treated.