%0 Journal Article
%T Functions measuring smoothness and the constants in Jackson--Stechkin theorem
%A A. G. Babenko
%A Yu. V. Kryakin
%J Mathematics
%D 2008
%I arXiv
%X This 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.
%U http://arxiv.org/abs/0809.0178v1