  In this paper, two double Jordan-type inequalities are introduced that
generalize some previously established inequalities. As a result, some new
upper and lower bounds and approximations 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. Based on this approach, some optimal approximations of the sinc
function are derived by determining the corresponding minimax approximants.
