منابع مشابه
Minimax Theorems
We suppose that X and Y are nonempty sets and f : X × Y → R. A minimax theorem is a theorem that asserts that, under certain conditions , inf Y sup X f = sup X inf Y f, that is to say, inf y∈Y sup x∈X f (x, y) = sup x∈X inf y∈Y f (x, y). The purpose of this article is to give the reader the flavor of the different kind of mini-max theorems, and of the techniques that have been used to prove the...
متن کاملTopological Minimax Theorems: Old and New
We review and extend the main topological minimax theorems based on connectedness that have been developed over the years since the pioneering paper of Wu (1959). It is shown in particular that the topological minimax theorems of Geraghty and Lin (1984) are essentially a rediscovery of much earlier results of Tuy (1974), while the latter can be derived from a minimax theorem recently developed ...
متن کاملGeneralized Minimax Theorems On Nonconvex Domains∗
In this paper, the author considers generalized minimax theorems for vector set-valued mappings using Fan-KKM theorem on nonconvex domains of Hausdorff topological vector spaces.
متن کاملMinimax Theorems in Probabilistic Metric Spaces
The minimax problem is of fundamental importance in nonlinear analysis and, especially, plays an important role in mathematical economics and game theory. The purpose of this paper is to obtain some minimax theorems for mixed lowerupper semi-continuous functions in probabilistic metric spaces which extend the minimax theorems of von Neumann types [1, 3, 4, 5, 6, 8, 10, 11, 12]. As applications,...
متن کاملConvexity beyond Vector Spaces, Alternative Theorems and Minimax Equality
The concept of convexlike (concavelike) functions was introduced by Ky Fan (1953), who has proved the rst minimax theorem without linear structure of the underlying spaces. Further extensions or generalizations of this concept have been used later in optimization and decision theory, but the most signiicant applications are in the framework of the game theory, where the strategy spaces are not ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1953
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.39.1.42