Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2011, Article ID 187052, 29 pages doi:10.1155/2011/187052 Research Article A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces Pongsakorn Sunthrayuth 1, 2 and Poom Kumam 1, 2 1 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand 2 Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand Correspondence should be addressed to Poom Kumam, poom.kum@kmutt.ac.th Received 4 April 2011; Accepted 8 May 2011 Academic Editor: Yansheng Liu Copyright q 2011 P. Sunthrayuth and P. Kumam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction In the theory of variational inequalities and variational inclusions, the development of an efficient and implementable iterative algorithm is interesting and important. The important generalization of variational inequalities called variational inclusions, have been extensively studied and generalized in different directions to study a wide class of problems arising in optimization, nonlinear programming, finance, economics, and applied sciences. Variational inequalities are being used as a mathematical programming tool in modeling a wide class of problems arising in several branches of pure and applied mathematics. Several numerical techniques for solving variational inequalities and the related optimization problem have been considered by many authors. Throughout this paper, we denoted by N and R  the set of all positive integers and all positive real numbers, respectively. Let X be a real Banach space and X ∗ be its dual space. Let