Approximation of continuous periodic functions by de la Vallee Poussin sums

Abstract

We obtain an estimate of the deviation of de la Vallee Poussin sums V_{n,n/2}(f;x) from continuous functions f, expressed in terms of values of theirs modulus of continuity. It is established that this estimate can't be improved by using the well-known analogue of the Lebesgue inequality for de la Vallee Poussin sums