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
Department of Mathematics, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China
Received 9 November 2005; Accepted 21 January 2006
Copyright © 2006 Heng-You Lan. 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 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.