Minimax and variational inequalities for compact spaces

McClendon, J. F.

doi:10.1090/S0002-9939-1983-0719003-2

Minimax and variational inequalities for compact spaces
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Proc. Amer. Math. Soc. 89 (1983), 717-721 Request permission

Abstract:

The minimax inequality ${\min _x}{\sup _y}f(x,y) \leqslant {\sup _x}f(x,x)$ ,proved by K. Fan for convex spaces, is proved here for certain contractible and acyclic spaces. Some variational inequality and fixed point theorems are deduced.

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On non-contractibel valued multifunctions

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