Los teoremas de Fr\'echet, Montel y Popoviciu y los grafos de los polinomios discontinuos

TL;DR

This paper introduces the regularity theory of functional equations, focusing on Fréchet's equation and honoring Tiberiu Popoviciu's contributions, with a particular emphasis on the properties of discontinuous polynomials and their graphical representations.

Contribution

It provides an overview of the regularity theory related to Fréchet's functional equation and highlights the work of Tiberiu Popoviciu in the context of discontinuous polynomials.

Findings

Analysis of the properties of discontinuous polynomials

Connections between functional equations and graph structures

Historical overview of key theorems in the field

Abstract

This paper is an introduction to the regularity theory of functional equations, motivated by the study of Fr\'{e}chet's functional equation. Another main goal is to honor the work in functional equations of the Romanian mathematician Tiberiu Popoviciu.