General Nonlinear Random Equations with Random Multivalued Operator in Banach Spaces

• Main Authors: Cho YeolJe, Lan Heng-You, Xie Wei
• Format: Article
• Language: English
• Published: SpringerOpen 2009-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2009/865093

<p/> <p>We introduce and study a new class of general nonlinear random multivalued operator equations involving generalized <inline-formula> <graphic file="1029-242X-2009-865093-i1.gif"/></inline-formula>-accretive mappings in Banach spaces. By using the Chang's lemma and the resolvent operator technique for generalized <inline-formula> <graphic file="1029-242X-2009-865093-i2.gif"/></inline-formula>-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 <inline-formula> <graphic file="1029-242X-2009-865093-i3.gif"/></inline-formula>-uniformly smooth Banach spaces. The results presented in this paper improve and generalize some known corresponding results in iterature.</p>