Fixed point theorems and applications

• Grant number: 25/02043-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2025
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eduardo Rosinato Longa
• Grantee: Leandro Gonçalves Ribeiro
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

We will study three classical fixed point theorems: Banach, Schauder and Kakutani. To do this, it will be necessary to establish a solid foundation on the theory of Metrics Spaces and Functional Analysis, areas any mathematician -- pure or applied -- has to be familiar with. As applications of these results, we will explore the classical theorem of existence and uniqueness of ordinary differential equations and interesting cases of the celebrated Nash equilibrium theorem.