Estimation d'erreur de certaines règles de quadrature impliquant au plus cinq points

Abstract

In this memory, we will focus on the study of Newton-Cotes type integral inequalities. In the first chapter, we will review some basic definitions, such as approximate integration and the quadrature formulation of simple interpolation type, as well as some known formulas that we will need in the following chapters. In the second chapter, we will study Newton-Cotes type inequalities for functions of bounded variation, dedicating part of this chapter to new results in this field. The third chapter will be devoted to the study of Newton-Cotes type inequalities for lipschitzian and bounded functions. As for the fourth chapter, it will be dedicated to the study of Newton-Cotes type inequalities for functions whose first derivatives belong to the 𝐿 𝑝 space. In the last chapter, we will focus on the study of Newton-Cotes type inequalities for functions whose first derivatives are extended s-convex