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.
Pongsakorn Sunthrayuth. Poom Kumam. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces." J. Appl. Math. 2011 1 - 29, 2011. https://doi.org/10.1155/2011/187052