Sur la théorie de la convexité et ses applications

Abstract

This thesis is devoted to the study of convex theory and its applications. The aim of this work is to develop a general study of convex sets and convex functions. This memory is divided into three chapters. First chapter provides some additional definitions and results that will be used later. In the second chapter, we study convex sets and convex functions. We study properties of continuity, semi-continuity and differentiation. In the third chapter we present application on convexity, the results of existence and the singularity of the minimum limits of convex functions.