Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions

Basing on Fourier’s trigonometric sums and the classical de la Vallée-Poussin means, we introduce the repeated de la Vallée-Poussin means. Under study are the approximation properties of the repeated means for piecewise smooth functions. We prove that the repeated means achieve the rate of approximation for the discontinuous piecewise smooth functions which is one or two order higher than the classical de la Vallée-Poussin means and the partial Fourier sums respectively.