Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 81261, 17 pages
doi:10.1155/JIA/2006/81261

Projection iterative approximations for a new class of general random implicit quasi-variational inequalities

Heng-You Lan

 Department of Mathematics, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China
Received 9 November 2005; Accepted 21 January 2006

Abstract

We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stability of a new perturbed Ishikawa iterative algorithm for solving a class of generalized random nonlinear implicit quasi-variational inequalities involving random single-valued mappings. The results presented in this paper improve and extend the earlier and recent results.