Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence Theorems of Solutions for a System of Nonlinear Inclusions with an Application | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID56161 12 pages doi 2007 56161 Research Article Existence Theorems of Solutions for a System of Nonlinear Inclusions with an Application Ke-Qing Wu Nan-Jing Huang and Jen-Chih Yao Received 7 June 2006 Revised 3 November 2006 Accepted 18 December 2006 Recommended by H. Bevan Thompson By using the iterative technique and Nadler s theorem we construct a new iterative algorithm for solving a system of nonlinear inclusions in Banach spaces. We prove some new existence results of solutions for the system of nonlinear inclusions and discuss the convergence of the sequences generated by the algorithm. As an application we show the existence of solution for a system of functional equations arising in dynamic programming of multistage decision processes. Copyright 2007 Ke-Qing Wu et al. 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. 1. Introduction It is well known that the iterative technique is a very important method for dealing with many nonlinear problems see . 1-4 . Let E be a real Banach space let X be a nonempty subset of E and let A B X X X - E be two nonlinear mappings. Chang and Guo 5 introduced and studied the following nonlinear problem in Banach spaces A u u u B u u u which has been used to study many kinds of differential and integral equations in Banach spaces. If A B then problem reduces to the problem considered by Guo and Lakshmikantham 1 . On the other hand Huang et al. 6 introduced and studied the problem of finding u E X x E Su and y E Tu such that A y x u 2 Journal of Inequalities and Applications where A X X X X is a nonlinear mapping and s T X 2X are two set-valued mappings. They constructed an iterative algorithm for solving this problem and gave an application to the problem
