On a relation between Schur, Hardy-Littlewood-Pólya and Karamata’s theorem and an inequality of some products of x p − 1 derived from the Furuta inequality

Keiichi Watanabe

doi:10.1186/1029-242x-2013-137

Abstract

We show a functional inequality of some products of x p −1 as an application of an operator inequality. Furthermore, we will show it can be deduced from a classical theorem on majorization and convex functions.MSC:26D07, 26A09, 26A51, 39B62, 47A63.

Highlights

1 Introduction It is easy to see the inequalities for arbitrary < x if they are provided as the matter to be proved
In Section, we prove a certain functional inequality as mentioned above, the efficiency and possible applications to other branches of mathematics are still to be clarified
In Section, we show that the functional inequality derived in Section can be deduced from Schur, Hardy-Littlewood-Pólya and Karamata’s theorem on majorization and convex functions

Summary

Introduction

It is easy to see the inequalities or for arbitrary < x if they are provided as the matter to be proved. Introduction It is easy to see the inequalities for arbitrary < x if they are provided as the matter to be proved. Example The following inequality does not hold on an interval contained in < x. In Section , we show that the functional inequality derived in Section can be deduced from Schur, Hardy-Littlewood-Pólya and Karamata’s theorem on majorization and convex functions.

Results

Conclusion