Lebesgue type inequalities for interpolation analogues of Valle Poussin sums on sets of infinitely differentiable functions

Abstract

We obtain estimates of of deviations of interpolation analogues of de la Valle Poussin sums from the functions that belong to the sets $C^{\psi}_{\beta}C$ and are represented through the best approximations of $(\psi,\beta)$-derivatives of these functions by trigonometric polynomials in the uniform metric.