- Tytuł:
- Minimax theorems without changeless proportion
- Autorzy:
-
Chu, Liang-Ju
Tsai, Chi-Nan - Powiązania:
- https://bibliotekanauki.pl/articles/729509.pdf
- Data publikacji:
- 2003
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
minimax theorems
t-convex functions
upward functions
jointly upward functions
X-quasiconcave sets - Opis:
-
The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds:
$inf_{y∈Y} sup_{x∈X} f(x,y) ≤ sup_{x∈X} inf_{y∈Y} g(x,y)$.
We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition:
$sup_{x∈X} f(x,y) ≤sup_{x∈X}g(x,y)$, ∀y ∈ Y.
However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties of multifunctions, we define X-quasiconcave sets, so that we can extend the two functions minimax theorem to the graph of the multifunction. In fact, we get the inequality:
$inf_{y∈T(X)} sup_{x∈T^{-1}(y)} f(x,y) ≤ sup_{x∈X} inf_{y∈T(x)} g(x,y)$,
where T is a multifunction from X to Y. - Źródło:
-
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2003, 23, 1; 55-92
1509-9407 - Pojawia się w:
- Discussiones Mathematicae, Differential Inclusions, Control and Optimization
- Dostawca treści:
- Biblioteka Nauki
Artykuł