Refinement of some moment inequalities

TL;DR

This paper improves existing convex and log-convex moment inequalities using positive semi-definite forms and discusses an open problem related to second-order refinements with applications in Information Theory.

Contribution

It introduces new refinements of moment inequalities and proposes an open problem for further research in second-order inequalities.

Findings

Refined convex and log-convex moment inequalities.

Established a new framework using positive semi-definite forms.

Presented an open problem with potential applications in Information Theory.

Abstract

In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is also stated with some applications in Information Theory.