International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 339-344
doi:10.1155/S0161171287000401
Iterative methods for nonlinear quasi complementarity problems
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.
Abstract
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 (u−m(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.