Copyright © 2010 Xin-kun Wu and Yun-zhi Zou. 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 system of random nonlinear generalized variational inclusions involving random fuzzy mappings and set-valued mappings with H(⋅,⋅)-monotonicity in two Hilbert spaces and develop a new algorithm which produces four random iterative sequences. We also discuss the existence of the random solutions to this new kind of system of variational inclusions and the convergence of the random iterative sequences generated by the algorithm.