Brauer's Fixed Point Theorem

2021 ◽  
Vol 8 (1) ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Simple Proof ◽  
Exchange Model ◽  
Existence Of Equilibrium ◽  
Economic Applications ◽  
Brouwer’S Fixed Point Theorem ◽  
Brouwer's Fixed Point Theorem

The primary goal of the paper is to deliver a simple proof of equivalence between Brouwer’s fixed point theorem and the existence of equilibrium in a simple exchange model with monotonic consumers. To achieve this end, we discuss some equivalent formulations of Brouwer’s theorem and prove additional ones, that are ’approximating’ in character or seem to be better suited for economic applications than the standard results.

A Brouwer Type Coincidence Theorem and the Fundamental Theorem of Algebra

1984 ◽  
Vol 27 (4) ◽  
pp. 478-480 ◽  
Author(s):  
M. M. Dodson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Simple Proof ◽  
Fundamental Theorem ◽  
Brouwer’S Fixed Point Theorem ◽  
Coincidence Theorem ◽  
Fundamental Theorem Of Algebra ◽  
Natural Generalisation ◽  
Brouwer's Fixed Point Theorem

AbstractIt is shown that a coincidence theorem which is a natural generalisation of Brouwer's fixed point theorem also gives a short and simple proof of the fundamental theorem of algebra.

scholarly journals Brouwer's Fixed Point Theorem with Isolated Fixed Points and His Fan Theorem

2012 ◽  
Vol 2012 ◽  
pp. 1-3
Author(s):  
Yasuhito Tanaka
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Brouwer’S Fixed Point Theorem ◽  
Fan Theorem ◽  
Brouwer's Fixed Point Theorem

We show that Brouwer’s fixed point theorem with isolated fixed points is equivalent to Brouwer’s fan theorem.

scholarly journals On Some Applications of Kakutani’s Fixed Point Theorem in Game Theory

2021 ◽  
Vol 66 (1) ◽  
pp. 49-69
Author(s):  
Md. Alamgir Hossain ◽  
◽  
Md. Zulfikar Ali ◽  
Md. Asaduzzaman ◽  
Md. Sazzad Hossain ◽  
...  
Keyword(s):  
Game Theory ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Research Work ◽  
Topological Properties ◽  
Set Functions ◽  
Brouwer’S Fixed Point Theorem ◽  
Effective Role ◽  
Brouwer's Fixed Point Theorem

In this paper, we discuss some major applications of Kakutani’s fixed point theorem in game theory. In the course of research work we mostly use the idea of mathematical set, functions, topological properties and Brouwer’s fixed point theorem to make the Kakutani’s fixed point theorem more conspicuous. In the key point of idea, we include how this theory can play the effective role to highlight new fixed point results and their applications in different fields of game theory.

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