Fixed point theorem and applications

• Grant number: 13/20665-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2013
• End date: November 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Pedro Jose Catuogno
• Grantee: Ian Dick de Paula
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM

Abstract

The fixed point theorem was established by S. Banach at the beginning of the twentieth century, it provides a standard way to prove existence and uniqueness of solutions to differential equations. The fixed point theorem is fundamental in order to establish the inverse function theorem and the Frobenius integrability. The purpose of this project is to introduce the candidate Ian Dick Paula in these matters which are of fundamental importance in the modern analysis.