Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A necessary and sufficient condition
for upper hemicontinuous
set-valued mappings without compact-values being upper demicontinuous

Authors: Gan-Shang Yang and George Xian-Zhi Yuan
Journal: Proc. Amer. Math. Soc. 126 (1998), 3539-3544
MSC (1991): Primary 47H04, 54C60
MathSciNet review: 1628436
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47H04, 54C60

Retrieve articles in all journals with MSC (1991): 47H04, 54C60

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

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
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society