In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions, as well as some Górniewicz-type fixed point theorems. Beyond the realm of monotonicity nor metrizability, the results derived here generalize and unify various earlier ones from the classic optimization theory. In the sequel, we shall deduce two versions of Nikaidô's coincidence theorem about Vietoris maps from different approaches.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1033,
author = {Liang-Ju Chu and Ching-Yan Lin},
title = {New versions on Nikaid\^o's coincidence theorem},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {22},
year = {2002},
pages = {79-95},
zbl = {1039.47035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1033}
}
Liang-Ju Chu; Ching-Yan Lin. New versions on Nikaidô's coincidence theorem. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 22 (2002) pp. 79-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1033/
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