Research Article General Nonlinear Random Equations with Random Multivalued Operator in Banach Space | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 865093 17 pages doi 2009 865093 Research Article General Nonlinear Random Equations with Random Multivalued Operator in Banach Spaces Heng-You Lan 1 Yeol Je Cho 2 and Wei Xie1 1 Department of Mathematics Sichuan University of Science Engineering Zigong Sichuan 643000 China 2 Department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 South Korea Correspondence should be addressed to YeolJe Cho yjcho@ Received 16 December 2008 Accepted 27 February 2009 Recommended by Jewgeni Dshalalow We introduce and study a new class of general nonlinear random multivalued operator equations involving generalized -accretive mappings in Banach spaces. By using the Chang s lemma and the resolvent operator technique for generalized -accretive mapping due to Huang and Fang 2001 we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative procedures with errors for this nonlinear random multivalued operator equations in -uniformly smooth Banach spaces. The results presented in this paper improve and generalize some known corresponding results in iterature. Copyright 2009 Heng-You Lan 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 and Preliminaries The variational principle has been one of the major branches of mathematical sciences for more than two centuries. It is a tool of great power that can be applied to a wide variety of problems in pure and applied sciences. It can be used to interpret the basic principles of mathematical and physical sciences in the form of simplicity and elegance. During this period the variational principles have played an important and significant part as a unifying influence
