 
Summary: PERGAMON Applied Mathematics Letters 12 (1999) 8992
The Existence of Nonlinear Inequalities
Q. H. Ansari
Department of Mathematics, A.M.U.
Aligarh 202 002, India
NgaiChing Wong and JenChih Yao
Department of Applied Mathematics, National Sun Yatsen University
Kaohsiung, Taiwan, R.O.C.
(Received and accepted May 1998)
AbstractThe object of this paper is to establish an existence result for nonlinear inequalities for
not necessarily pseudomonotone maps. As a consequence of our result, we give some existence results
for variational and variationallike inequalities. c 1999 Elsevier Science Ltd. All rights reserved.
KeywordsNonlinear inequalities, Variational inequality problems, Variationallike inequality
problems, Fixed points.
1. INTRODUCTION AND PRELIMINARIES
Let X be a real locally convex space with its dual X
and K be a nonempty convex subset of X.
Let : K × K  R be a bifunction and f X
. Gwinner [1] considered the problem of finding
u0 in K such that
