The order of approximation to functions of the Z?. Class by means of positive linear operators

Abstract

Let Cn (ϕ, α) be the upper bound for deviations of periodic functions which form the Zygmund class Zα,0 0<α<2 from a class of positive linear operators. A study is made of the conditions under which there exists a limit\(\mathop {\lim }\limits_{n \to \infty } \)nαCn(ϕ, α)=C(θ, α). An explicit expression is given for the functions C(ϕ,α).