O Teorema do Ponto Fixo de Banach para contrações e algumas aplicações

Abstract

This paper aims to address a brief concept of Metric Spaces in order to present and demonstrate Banach’s Fixed-Point Theorem in Euclidean Space-ndimensional Rn. In addition, display some of its applications, especially in the demonstration of Existence and Uniqueness of Solutions of Ordinary Differential Equations. For this, we had to first study essential concepts such as the Topological Aspects of Space Rn, Metric Spaces and Spaces Complete Metrics, in order to define Banach Spaces and then to enunciate, demonstrate and show some applications of the Banach’s Fixed-Point Theorem for contractions which tells us that if Rn is a complete metric space, every contraction f : Rn ! Rn has a single fixed point in Rn, that is, there exists a unique x 2 Rn such that f(x) = x.