Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and the minimax theorem for two-person zero-sum games: A constructive analysis
Abstract
In this paper we constructively prove Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and uniformly closed graph, and apply this result to prove the minimax theorem for two-person zero-sum games with finite strategies. We follow the Bishop style constructive mathematics.
Copyright © 2012 Yasuhito Tanaka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
Y. Tanaka, Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and the minimax theorem for two-person zero-sum games: A constructive analysis, Adv. Fixed Point Theory 2 (2012), 120–134.
BibTeX
@article{Tanaka2012,
author = {Tanaka, Yasuhito},
title = {Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and the minimax theorem for two-person zero-sum games: A constructive analysis},
journal = {Adv. Fixed Point Theory},
volume = {2},
year = {2012},
pages = {120--134},
doi = {}
}