Teorema de Banach, sobre pontos fixos de contrações

Abstract

The objective of this work is to enunciate and demonstrate Banach's Theorem, about fixed points of contractions, then presenting applications of this theorem in the resolution of a nonlinear equation and in the important demonstration of the Existence and Uniqueness Theorem of solution of the initial value problem. Essential concepts for the understanding of the Banach's Theorem, such as metric spaces, sequences and convergence in metric spaces, complete metric spaces, contractions and fixed points of contractions were discussed.