Reflection on Brouwer's Fixed Point Theorem

Essay from the year 2018 in the subject Mathematics - Algebra, grade: 2.5, , language: English, abstract: The Brouwer's Fixed Point Theorem is one of the most well known and important existence principles in mathematics. Since the theorem and its many equivalent formulations or extensions are powerful tools in showing the existence of solutions for many problems in pure and applied mathematics, many scholars have been studying its further extensions and applications. The Brouwer Theorem itself gives no information about the location of fixed points. However, effective ways have been developed to calculate or approximate the fixed points. Such techniques are important in various applications including calculation of economic equilibria. Because Brouwer Fixed Point Theorem has a significant role in mathematics, there are many generalizations and proofs of this theorem. In this paper, we will try to show several proves of Brouwer Fixed Point Theorem. First, let's take a look at Brouwer Theorem from real world illustrations. There are several real world examples, and we will take in consideration few of them.