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
Ngai-Ching Wong and Jen-Chih Yao
Department of Applied Mathematics, National Sun Yat-sen University
Kaohsiung, Taiwan, R.O.C.
(Received and accepted May 1998)
Abstract--The 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 variational-like inequalities. c 1999 Elsevier Science Ltd. All rights reserved.
Keywords--Nonlinear inequalities, Variational inequality problems, Variational-like 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  considered the problem of finding
u0 in K such that