O Teorema da aplicação inversa de Ekeland em espaços de Fréchet

Abstract

In this work, we study the Ekeland's inverse function theorem in Fr echet spaces, that was published by Ekeland [8] in 2011. Initially, we present an inverse function theorem in Banach spaces (that is more general than the classical inverse function theorem in Euclidian spaces), which proof is based on Banach's xed point theorem. After this, we present another inverse function theorem in Banach spaces, which proof was done by Ekeland from Ekeland's variational principle and some results in convex analysis. Finally, we present the Ekeland's inverse function theorem in Fr echet spaces, which proof is based on Ekeland's variational principle and other results in measure theory and convex analysis.