Journal of Applied Mathematics
Volume 2012 (2012), Article ID 590676, 21 pages
http://dx.doi.org/10.1155/2012/590676
Research Article

Existence and Stability of Iterative Algorithm for a System of Random Set-Valued Variational Inclusion Problems Involving ( 𝐴 , 𝑚 , 𝜂 )-Generalized Monotone Operators

Jittiporn Suwannawit1,2 and Narin Petrot1

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2The Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand

Received 18 January 2012; Accepted 25 March 2012

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Jittiporn Suwannawit and Narin Petrot. 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 class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called ( 𝐴 , 𝑚 , 𝜂 )-monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is also discussed.