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We obtain the estimates of steady rates of deviations of the de Vall\'{e}ePoussin sums and interpolation analogues of sums of Vall\'{e}e Poussin from thefunctions that belong to the space $C_{\bar{\beta}}^\psi L_s, \ 1\leqs\leq\infty$ and are represented through the best approximations of$(\psi,\bar{\beta})$-differentiable functions of this sort by trigonometricpolynomials in the metric $L_s$

Lebesgue-type inequalities for de la Vallee Poussin sums and their interpolation analogues on the sets $(\psi,\bar{\beta})$-differentiable functions