The stability of Ky Fan’s points
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- by Kok-Keong Tan, Jian Yu and Xian-Zhi Yuan PDF
- Proc. Amer. Math. Soc. 123 (1995), 1511-1519 Request permission
Abstract:
In this paper, inspired by the work of Fort, the stability of the set $F(f) = \{ y \in X:{\sup _{x \in X}}f(x,y) \leq 0\}$ (respectively, the set $F(A,f) = \{ y \in A:{\sup _{x \in A}}f(x,y) \leq 0\}$ ) with f varying (respectively, with both f and A varying) is studied where X is a non-empty compact convex subset of a Hausdorff topological vector space (respectively, X is a Hausdorff topological space and A is a non-empty compact subset of X ) and $f:X \times X \to \mathbb {R}$ is bounded.References
- Gerald Beer, On a generic optimization theorem of Petar Kenderov, Nonlinear Anal. 12 (1988), no. 6, 647–655. MR 945669, DOI 10.1016/0362-546X(88)90020-X
- Jens Peter Reus Christensen, Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings, Proc. Amer. Math. Soc. 86 (1982), no. 4, 649–655. MR 674099, DOI 10.1090/S0002-9939-1982-0674099-0
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- 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
- M. K. Fort Jr., Points of continuity of semi-continuous functions, Publ. Math. Debrecen 2 (1951), 100–102. MR 46636
- M. K. Fort Jr., Essential and non essential fixed points, Amer. J. Math. 72 (1950), 315–322. MR 34573, DOI 10.2307/2372035
- Petar S. Kenderov, Most of the optimization problems have unique solution, Parametric optimization and approximation (Oberwolfach, 1983) Internat. Schriftenreihe Numer. Math., vol. 72, Birkhäuser, Basel, 1985, pp. 203–216. MR 882205
- 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
- Bor-Luh Lin and Stephen Simons (eds.), Nonlinear and convex analysis, Lecture Notes in Pure and Applied Mathematics, vol. 107, Marcel Dekker, Inc., New York, 1987. MR 892775
- Kok-Keong Tan, Jian Yu, and Xian-Zhi Yuan, The stability of coincident points for multivalued mappings, Nonlinear Anal. 25 (1995), no. 2, 163–168. MR 1333820, DOI 10.1016/0362-546X(94)00223-5 —, The stability of production economies, J. Austral. Math. Soc. (to appear).
- Jian Yu, Essential weak efficient solution in multiobjective optimization problems, J. Math. Anal. Appl. 166 (1992), no. 1, 230–235. MR 1159649, DOI 10.1016/0022-247X(92)90338-E
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1511-1519
- MSC: Primary 47H99; Secondary 46A55, 47H04, 47N10, 49J40
- DOI: https://doi.org/10.1090/S0002-9939-1995-1239807-8
- MathSciNet review: 1239807