Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 728452, 15 pages
doi:10.1155/2010/728452
Research Article

A Generalized Nonlinear Random Equations with Random Fuzzy Mappings in Uniformly Smooth Banach Spaces

Nawitcha Onjai-Uea1,2 and Poom Kumam1,2

1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand
2Centre of Excellence in Mathematics, CHE, Sriayudthaya Road, Bangkok 10400, Thailand

Received 26 July 2010; Accepted 31 October 2010

Academic Editor: Yeol J. E. Cho

Copyright © 2010 Nawitcha Onjai-Uea and Poom Kumam. 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 the general nonlinear random ( 𝐻 , 𝜂 ) -accretive equations with random fuzzy mappings. By using the resolvent technique for the ( 𝐻 , 𝜂 ) -accretive operators, we prove the existence theorems and convergence theorems of the generalized random iterative algorithm for this nonlinear random equations with random fuzzy mappings in 𝑞 -uniformly smooth Banach spaces. Our result in this paper improves and generalizes some known corresponding results in the literature.