Some topological minimax theorems |
| |
Authors: | B R Frenkin |
| |
Institution: | (1) Central Institute of Mathematical Economics, Russian Academy of Sciences, Moscow |
| |
Abstract: | Two topological variants of the minimax theorem are proved with no restrictions on one of the spaces except for those related
to the function under consideration. The conditions concerning the behavior of the function deal only with the interval between
the maximin and minimax. As corollaries, we obtain the well-known theorems of Sion and Hoang-Tui on quasiconvex-quasiconcave
semicontinuous functions. The scheme of arguments goes back to the Hahn-Banach theorem and the separating hyperplane theorem.
It is shown how this scheme can be explicitly realized in the proof of the Hahn-Banach theorem.
Translated fromMaternaticheskie Zametki, Vol. 67, No. 1, pp. 141–149, January, 2000. |
| |
Keywords: | minimax and maximin quasiconvex and quasiconcave functions semicontinuous functions |
本文献已被 SpringerLink 等数据库收录! |
|