International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 339-344

Iterative methods for nonlinear quasi complementarity problems

Muhammad Aslam Noor

Mathematics Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received 13 April 1985; Revised 1 July 1986

Copyright © 1987 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 consider and study an iterative algorithm for finding the approximate solution of the nonlinear quasi complementarity problem of finding u ϵ k(u) such that Tu ϵ k*(u)  and  (um(u),Tu)=0 where m is a point-to-point mapping, T is a (nonlinear) continuous mapping from a real Hilbert space H into itself and k*(u) is the polar cone of the convex cone k(u) in H. We also discuss the convergence criteria and several special cases, which can be obtained from our main results.