# New versions on Nikaidô's coincidence theorem

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

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

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topLiang-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 -

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