Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 479-494

Auxiliary principle and fuzzy variational-like inequalities

S. S. Chang,1,2 D. O'Regan,3 K. K. Tan,4 and L. C. Zeng5

1Department of Mathematics, Yibin University, Sichuan, Yibin 644007, China
2Department of Mathematics, Sichuan University, Sichuan, Chengdu 610064, China
3Department of Mathematics, National University of Ireland, Galway, Ireland
4Department of Mathematics and Statistics, Dalhousie University, Nova Scotia, Halifax B3H 3J5, Canada
5Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 4 January 2004

Copyright © 2005 S. S. Chang et al. 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.


The purpose of this paper is to introduce the concept of fuzzy variational-like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy variational-like inequalities in Hilbert spaces. By using the general auxiliary principle technique, Ky Fan's KKM theorem, Nadler's fixed point theorem, and some new analytic techniques, some existence theorems and some iterative approximation schemes for solving this kind of fuzzy variational-like inequalities are established. The results presented in this paper are new and they generalize, improve, and unify a number of recent results.