Applications of pseudo-monotone operators

with some kind of upper semicontinuity

in generalized quasi-variational inequalities

on non-compact sets

Authors:
Mohammad S. R. Chowdhury and Kok-Keong Tan

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2957-2968

MSC (1991):
Primary 47H04, 47H05, 47H09, 47H10; Secondary 49J35, 49J40, 54C60

DOI:
https://doi.org/10.1090/S0002-9939-98-04436-0

MathSciNet review:
1459115

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a topological vector space and be a non-empty subset of . Let and be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point and a point such that for all . We shall use Chowdhury and Tan's 1996 generalized version of Ky Fan's minimax inequality as a tool to obtain some general theorems on solutions of the GQVI on a paracompact set in a Hausdorff locally convex space where the set-valued operator is either strongly pseudo-monotone or pseudo-monotone and is upper semicontinuous from to the weak-topology on for each non-empty finite subset of .

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Additional Information

**Mohammad S. R. Chowdhury**

Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

Email:
mohammad@mscs.dal.ca

**Kok-Keong Tan**

Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5

Email:
kktan@mscs.dal.ca

DOI:
https://doi.org/10.1090/S0002-9939-98-04436-0

Keywords:
Generalized quasi-variational inequality,
locally convex space,
partition of unity,
paracompact sets,
lower semi-continuous,
upper semi-continuous,
strongly pseudo-monotone,
pseudo-monotone and monotone operators

Received by editor(s):
May 15, 1996

Received by editor(s) in revised form:
March 7, 1997

Additional Notes:
The work of the second author was partially supported by NSERC of Canada under grant A-8096.

Communicated by:
Dale Alspach

Article copyright:
© Copyright 1998
American Mathematical Society