Exponential Polynomials and Stratification in the Theory of Analytic Inequalities

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 [1] through two applications, referring to inequalities from papers [2] and [3].

Jordan-Type Inequalities and Stratification

“…Namely, by applying stratification, it is possible to extend the inequality (7) so that the parameter n can be a positive real number. The extension of inequalities for real parameters has recently been the subject of various studies [24][25][26][27], see also [28][29][30][31]. Additionally, we provide the best constants for this type of Jordan's inequality, as well as an analysis of upper and lower bounds and minimax approximations of the sinc x function based on the inequalities (2), ( 3), ( 4), (5), as well as on the newly obtained inequalities.…”

Jordan-Type Inequalities and Stratification

“…Namely, by applying stratification, it is possible to extend the inequality (7) so that the parameter n can be a positive real number. The extension of inequalities for real parameters has recently been the subject of various studies [24][25][26][27]; see also [28][29][30][31]. Additionally, we provide the best constants for this type of Jordan's inequality, as well as an analysis of the upper and lower bounds and minimax approximations of the sinc x function based on the inequalities (2)-( 5), as well as on the newly obtained inequalities.…”