The stability of Ky Fan’s points

Tan, Kok-Keong; Yu, Jian; Yuan, Xian-Zhi

doi:10.1090/S0002-9939-1995-1239807-8

The stability of Ky Fan’s points
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by Kok-Keong Tan, Jian Yu and Xian-Zhi Yuan

Proc. Amer. Math. Soc. 123 (1995), 1511-1519

DOI: https://doi.org/10.1090/S0002-9939-1995-1239807-8

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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.

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