Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 4, Pages 381-391

Some new deterministic and random variational inequalities and their applications

Xian-Zhi Yuan1,2 and Jean-Marc Roy3

1The University of Queensland, Department of Mathematics, Brisbane 4072, QLD, Australia
2Dalhousie University, Department of Mathematics, N.S., Halifax B3H 3J5, Canada
3Centre Universitaire de Shippagan, Department of Mathematics, N.B., Shippagan E0B 2P0, Canada

Received 1 June 1994; Revised 1 July 1995

Copyright © 1995 Xian-Zhi Yuan and Jean-Marc Roy. 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.


A non-compact deterministic variational inequality which is used to prove an existence theorem for saddle points in the setting of topological vector spaces and a random variational inequality. The latter result is then applied to obtain the random version of the Fan's best approximation theorem. Several random fixed point theorems are obtained as applications of the random best approximation theorem.