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Title

New versions on Nikaidô's coincidence theorem

Authors 1, 1

Affiliations

  1. Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, Republic of China

Abstract

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.

Keywords

ENG
Vietoris map, Nikaidô's coincidence theorem, Fan-type element, Górniewicz-type fixed point theorem, coincidence, variational inequality, acyclic multifunction, partition of unity, local intersection property, KKM mapping, locally selectionable multifunction

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2002/22/1
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Pages:
79-95
Main language of publication
English
Received
2002-03-05
Accepted
2002-06-25
Published
2002

DOI: 10.7151/dmgt.1033

Exact and natural sciences