An application of a method of summability to Fourier series

Abstract

Applying $r$-repeated de la Vallée Poussin sums, we have proved four theorems which show the upper bound of the $r$-repeated de la Vall'ee Poussin kernel, their convergence at a point, the deviation between a continuous function and the $r$-repeated de la Vallée Poussin sums of partial sums of its Fourier series, and finally we determine the degree of approximation of functions belonging to ordinary Lipschitz class.