2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168119This paper is devoted to the equivalence of two type direct theorems in Approximation Theory: a) for smooth functions (Favard's estimates). b) for arbitrary continuous function (Jackson--Stechkin estimates). Specifically, we will show that Jackson--Stechkin inequality with optimal respect to the order of smoothness constants follows from Favard's inequality.6 pagesClassical Analysis and ODEs41A17, 41A44, 42A10text