Applications of pseudomonotone operators with some kind of upper semicontinuity in generalized quasivariational inequalities on noncompact sets
Authors:
Mohammad S. R. Chowdhury and KokKeong Tan
Journal:
Proc. Amer. Math. Soc. 126 (1998), 29572968
MSC (1991):
Primary 47H04, 47H05, 47H09, 47H10; Secondary 49J35, 49J40, 54C60
MathSciNet review:
1459115
Fulltext PDF Free Access
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Abstract: Let be a topological vector space and be a nonempty subset of . Let and be two maps. Then the generalized quasivariational 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 setvalued operator is either strongly pseudomonotone or pseudomonotone and is upper semicontinuous from to the weaktopology on for each nonempty 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
KokKeong Tan
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email:
kktan@mscs.dal.ca
DOI:
http://dx.doi.org/10.1090/S0002993998044360
PII:
S 00029939(98)044360
Keywords:
Generalized quasivariational inequality,
locally convex space,
partition of unity,
paracompact sets,
lower semicontinuous,
upper semicontinuous,
strongly pseudomonotone,
pseudomonotone 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 A8096.
Communicated by:
Dale Alspach
Article copyright:
© Copyright 1998 American Mathematical Society
