The order of approximation to functions of the $Z_\alpha$. Class by means of positive linear operators

Let $C_n(\varphi,\alpha)$ be the upper bound for deviations of periodic functions which form the Zygmund class $Z_\alpha$, $0<\alpha<2$ from a class of positive linear operators. A study is made of the conditions under which there exists a limit $\lim\limits_{n\to\infty}n^\alpha C_n(\varphi,\alpha)$. An explicit expression is given for the functions $C(\varphi,\alpha)$.