Exponential Polynomials and Stratification in the Theory of Analytic Inequalities

TL;DR

This paper introduces a method using Maclaurin series to prove positivity of mixed exponential polynomial inequalities and explores their relation to stratified function families through applications to existing inequalities.

Contribution

It presents a novel approach for verifying positivity of MEP inequalities and connects them to stratification concepts in analytic inequalities.

Findings

Method effectively proves positivity over positive intervals.

Links MEPs with stratified function families.

Applied to classical inequalities from literature.

Abstract

This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals using the Maclaurin series to approximate the exponential function precisely. Additionally, we discuss the relation between MEPs and stratified families of functions from [Malesevic_Mihailovic_2021] through two applications, referring to inequalities from papers [Wu_Zhang_2004] and [Chesneau_Bagul_Dhaigude_2022].