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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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