On the best polynomial approximation of $(\psi,\beta)$-differentiable functions in $L_2$ space

On the classes $L^{\psi}_{\beta,2}$ exact estimates have been obtained for the values of the best polynomial approximations of $(\psi,\beta)$-differentiable functions, expressed by the averages modulus of continuity $\widehat{\omega}(f^{\psi}_{\beta},t)$ with a weight $\xi(t)$. This modulus was introduced by K.V. Runovski and H.J. Schmeisser.