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.
@article{bwmeta1.element.bwnjournal-article-cmv63i2p233bwm,
author = {Xie Ding and Kok-Keong Tan},
title = {A minimax inequality with applications to existence of equilibrium point and fixed point theorems},
journal = {Colloquium Mathematicae},
volume = {63},
year = {1992},
pages = {233-247},
zbl = {0833.49009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv63i2p233bwm}
}
Ding, Xie; Tan, Kok-Keong. A minimax inequality with applications to existence of equilibrium point and fixed point theorems. Colloquium Mathematicae, Tome 63 (1992) pp. 233-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv63i2p233bwm/
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