New versions on Nikaidô's coincidence theorem

Liang-Ju Chu; Ching-Yan Lin

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2002)

  • Volume: 22, Issue: 1, page 79-95
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Liang-Ju Chu, and Ching-Yan Lin. "New versions on Nikaidô's coincidence theorem." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 22.1 (2002): 79-95. <http://eudml.org/doc/271465>.

@article{Liang2002,
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.},
author = {Liang-Ju Chu, Ching-Yan Lin},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {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; fixed point; multifunction KKM mapping},
language = {eng},
number = {1},
pages = {79-95},
title = {New versions on Nikaidô's coincidence theorem},
url = {http://eudml.org/doc/271465},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Liang-Ju Chu
AU - Ching-Yan Lin
TI - New versions on Nikaidô's coincidence theorem
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2002
VL - 22
IS - 1
SP - 79
EP - 95
AB - 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.
LA - eng
KW - 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; fixed point; multifunction KKM mapping
UR - http://eudml.org/doc/271465
ER -

References

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