  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].
