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Sur un principe géométrique en analyse convexe

Andrzej Granas, Marc Lassonde (1991)

Studia Mathematica

In this note we present we present a new elementary approach in the theory of minimax inequalities. The proof of the main result (called the geometric principle) uses only some simple properties of convex functions. The geometric principle (which is equivalent to the well-known lemma of Klee [13]) is shown to have numerous applications in different areas of mathematics.

The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

George Isac, George Xian-Zhi Yuan (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...

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