APPROXIMATION OF A CONTINUOUS FUNCTION BY CESARO MEANS OF ITS FOURIER SERIES

Abstract

For a continuous function f(x) with a period 2π, M. Rietz proved that the αth order Cesaro means of the partial sums of its Fourier series uniformly approximated to f ( x ). This paper gives the degree of approximation. We use { S n ( x )} to denote the partial sums of the Fourier series of f(x) and ( C , α ), the αth order Cesaro means. Furthermore we define