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A necessary and sufficient condition for upper hemicontinuous set-valued mappings without compact-values being upper demicontinuous
Author(s):
Gan-Shang
Yang;
George
Xian-Zhi
Yuan
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3539-3544.
MSC (1991):
Primary 47H04, 54C60
MathSciNet review:
1628436
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Abstract:
The purpose of this article is to give a characterization of an upper hemicontinuous mapping with non-empty convex values being upper demicontinuous, i.e., we show that an upper hemicontinuous set-valued mapping with non-empty convex values (not necessarily compact-valued) is upper demicontinuous if and only if the set-valued mapping has no interior asymptotic plane.
References:
- 1.
- J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, 1984. MR 87a:58002
- 2.
- J. P. Aubin and H. Frankowska, Set-valued Analysis, Birkhäuser, Boston, 1990. MR 91d:49001
- 3.
- K. Fan, A minimax inequality and applications, Inequalities III, Proceedings of Third Symposium on Inequalities (O. Shisha, ed.), Academic Press, New York, 1972, pp. 103-113. MR 49:5779
- 4.
- E. Klein and A. C. Thompson, Theory of Correspondences: including applications to mathematical economics, John Wiley and Sons, 1984. MR 86a:90012
- 5.
- M. H. Shih and K. K. Tan, Covering theorems of convex sets related to fixed point theorems, Nonlinear and Convex Analysis-Proceedings in Honor of Ky Fan (B. L. Lin and S. Simons, eds.), Marcel Dekker, Inc., 1987, pp. 235-244. MR 88g:46019
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Additional Information:
Gan-Shang
Yang
Affiliation:
Department of Mathematics, Yunnan National Institute, Kunming, China 650031
George
Xian-Zhi
Yuan
Affiliation:
Department of Mathematics, The University of Queensland, Brisbane, Queensland, Australia 4072
Email:
xzy@maths.uq.edu.au
DOI:
10.1090/S0002-9939-98-05082-5
PII:
S 0002-9939(98)05082-5
Keywords:
Upper semicontinuous,
upper hemicontinuous,
upper demicontinuous,
asymptotic plane,
interior asymptotic plane
Received by editor(s):
February 26, 1997
Additional Notes:
This project was supported in part by the Australian Research Council.
Communicated by:
David R. Larson
Copyright of article:
Copyright
1998,
American Mathematical Society
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