Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 1, Pages 43-56

On certain classes of variational inequalities and related iterative algorithms

Muhammad Aslam Noor

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

Received 1 October 1994; Revised 1 October 1995

Copyright © 1996 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 some new classes of variational inequalities and Wiener-Hopf equations. Essentially using the projection technique, we establish the equivalence between the multivalued general quasi-variational inequalities and the multivalued implicit Wiener-Hopf equations. This equivalence enables us to suggest and analyze a number of iterative algorithms for solving multivalued general quasi-variational inequalities. We also consider the auxiliary principle technique to prove the existence of a unique solution of the variational-like inequalities. This technique is used to suggest a general and unified iterative algorithm for computing the approximate solution. Several special cases which can be obtained from our main results are also discussed. The results proved in this paper represent a significant refinement and improvement of the previously known results.