Uma introdução às funções convexas

Abstract

This dissertation presents an introduction to convex functions of one real variable. After studying the concept of convex set, the notion of convex function is considered. Several theoretical results related to characterizations and properties of convex functions are presented. As an application of these results, some generalizations and relationships between means of positive numbers are explored and alternative proofs of means inequalities presented in the book of Discrete Mathematics of PROFMAT collection, are developed. In addition, is presented an exploration on the problem of decomposition of a function as the difference of convex functions, based on the concept of total variation of a function.