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 A New System of Generalized Nonlinear Mixed Variational Inclusions in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 908490 15 pages doi 2010 908490 Research Article A New System of Generalized Nonlinear Mixed Variational Inclusions in Banach Spaces Jian Wen Peng College of Mathematics and Computer Science Chongqing Normal University Chongqing Sichuan 400047 China Correspondence should be addressed to Jian Wen Peng jwpeng6@ Received 5 July 2009 Accepted 14 September 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 Jian Wen Peng. 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 and study a new system of generalized nonlinear mixed variational inclusions in real -uniformly smooth Banach spaces. We prove the existence and uniqueness of solution and the convergence of some new n-step iterative algorithms with or without mixed errors for this system of generalized nonlinear mixed variational inclusions. The results in this paper unify extend and improve some known results in literature. 1. Introduction Variational inclusion problems are among the most interesting and intensively studied classes of mathematical problems and have wide applications in the fields of optimization and control economics and transportation equilibrium as well as engineering science. For the past years many existence results and iterative algorithms for various variational inequality and variational inclusion problems have been studied. For details see 1-25 and the references therein. Recently some new and interesting problems which are called to be system of variational inequality problems were introduced and studied. Pang 1 Cohen and Chaplais 2 Bianchi 3 and Ansari and Yao 4 considered a system of scalar variational inequalities and Pang showed that the traffic equilibrium problem the spatial equilibrium problem the Nash .