Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 79-93

On a class of multivalued variational inequalities

Muhammad Aslam Noor

King Sand University, Mathematics Department, College of Science, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 1 October 1995; Revised 1 June 1996

Copyright © 1998 Muhammad Aslam Noor. 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.


In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These variational inequalities include as special cases, the previously known classes of variational inequalities. Using projection techniques, we show that multivalued variational inequalities are equivalent to fixed point problems and Wiener-Hopf equations. These alternate formulations are used to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to study the existence of a solution of multivalued variational inequalities and suggest a novel iterative algorithm. In addition, we have shown that the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.