Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 865093, 17 pages
doi:10.1155/2009/865093
Research Article

General Nonlinear Random Equations with Random Multivalued Operator in Banach Spaces

Heng-You Lan,1 Yeol Je Cho,2 and Wei Xie1

1Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, China
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea

Received 16 December 2008; Accepted 27 February 2009

Academic Editor: Jewgeni Dshalalow

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.

Abstract

We introduce and study a new class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces. By using the Chang's lemma and the resolvent operator technique for generalized m-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 q-uniformly smooth Banach spaces. The results presented in this paper improve and generalize some known corresponding results in iterature.