Geodesic
A minimax inequality with applications to existence of equilibrium point and fixed point theorems
Colloquium Mathematicum, Tome 63 (1992) no. 2, pp. 233-247.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an equilibrium point in a one-person game. Next, by applying the minimax inequality, we present some fixed point theorems for set-valued inward and outward mappings on a non-compact convex set in a topological vector space. These results generalize the corresponding results due to Browder [5], Jiang [11] and Shih Tan [15] in several aspects.
DOI : 10.4064/cm-63-2-233-247

Xie Ding 1 ; Kok-Keong Tan 1

1 
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Xie Ding; Kok-Keong Tan. A minimax inequality with applications to existence of equilibrium point and fixed point theorems. Colloquium Mathematicum, Tome 63 (1992) no. 2, pp. 233-247. doi : 10.4064/cm-63-2-233-247. http://geodesic.mathdoc.fr/articles/10.4064/cm-63-2-233-247/

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