Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 3, Pages 283-294

Iterative resolvent methods for general mixed variational inequalities

Muhammad Aslam Noor1 and Khalida Inayat Noor2

1Etisalat College of Engineering, P. O. Box 980, Sharjah, United Arab Emirates
2United Arab Emirates University, Department of Mathematics and Computer Science, P.O. Box 17551, Al-Ain, United Arab Emirates

Received 1 November 2002; Revised 1 September 2003

Copyright © 2003 Muhammad Aslam Noor and Khalida Inayat 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 use the technique of updating the solution to suggest and analyze a class of new self-adaptive splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Proof of convergence is very simple. Since general mixed variational include variational inequalities and complementarity problems as special cases, our results continue to hold for these problems.