Functions of class Lip( α, p) and their Taylor mean

Abstract

The object of this paper is to study the rapidity of convergence of the Taylor mean of the Fourier series of ƒ(x) when ƒ(x) belongs to the class Lip( α, p). We show that it is of Jackson order provided that a suitable integrability condition is imposed upon the function ϑ x(t) = 1 2 {ƒ(x + t) − 2ƒ(x) + ƒ(x − t)} .