Jordan-Type Inequalities and Stratification

Abstract

In this paper, two double Jordan-type inequalities are introduced based on the papers [1]-[5]. These inequalities generalize the inequalities obtained in [1]-[5]. As a result, some new upper and lower bounds of the sinc function are obtained. This extension of Jordan’s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions elaborated in [6]. Based on this approach, some optimal approximations of the sinc function are derived by determining corresponding minimax approximants, also described in the paper [6].