A necessary and sufficient condition for upper hemicontinuous set-valued mappings without compact-values being upper demicontinuous
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- by Gan-Shang Yang and George Xian-Zhi Yuan PDF
- Proc. Amer. Math. Soc. 126 (1998), 3539-3544 Request permission
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
- Jean-Pierre Aubin and Ivar Ekeland, Applied nonlinear analysis, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 749753
- Jean-Pierre Aubin and Hélène Frankowska, Set-valued analysis, Systems & Control: Foundations & Applications, vol. 2, Birkhäuser Boston, Inc., Boston, MA, 1990. MR 1048347
- Ky Fan, A minimax inequality and applications, Inequalities, III (Proc. Third Sympos., Univ. California, Los Angeles, Calif., 1969; dedicated to the memory of Theodore S. Motzkin), Academic Press, New York, 1972, pp. 103–113. MR 0341029
- Erwin Klein and Anthony C. Thompson, Theory of correspondences, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1984. Including applications to mathematical economics; A Wiley-Interscience Publication. MR 752692
- Mau-Hsiang Shih and Kok-Keong Tan, Covering theorems of convex sets related to fixed-point theorems, Nonlinear and convex analysis (Santa Barbara, Calif., 1985) Lecture Notes in Pure and Appl. Math., vol. 107, Dekker, New York, 1987, pp. 235–244. MR 892795
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
- 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 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3539-3544
- MSC (1991): Primary 47H04, 54C60
- DOI: https://doi.org/10.1090/S0002-9939-98-05082-5
- MathSciNet review: 1628436