Ponto fixo de banach aplicado às funções implícitas e à informática.

Abstract

In this work, we will present Banach’s Fixed Point Theorem and some of its various applica- tions in implicitly defined functions and in computing. For this, we will use the Topological notions in Metric Spaces and the concept of differentiability in Euclidean spaces. As for the area of computing, we will bring the famous Internet search engine “Google” as an example of the application of this theorem. In addition, its proof produces a method, known as Newton- Raphson, which is rich in information that enabled us to elaborate a software that approaches the roots of some functions.