Contents

A collection of new integral inequalities involving sub-multiplicative functions

Author(s): Christophe Chesneau1
1Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France
Copyright © Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this article, we establish new integral inequalities involving sub-multiplicative functions. We first derive several inequalities of primitive type, followed by new inequalities of the convolution product type. We also obtain integral bounds for functions evaluated on the product of two variables. Finally, we study double integral inequalities and their variations. Simple examples are used to illustrate the theory. The understanding of integral inequalities under submultiplicative assumptions is thus deepened, and some new ideas for further research in mathematical analysis are provided.

Keywords: sub-multiplicativity, integral inequalities, primitives, convolution product, double integral, polar change of variables