Approximation by nonlinear fourier basis in generalized holder spaces

Abstract

In this paper, the value of deviation of a function f from its nth generalized de la Vallee-Poussin mean V-n(alpha)(lambda, f) with respect to the nonlinear trigonometric system is estimated for the classes of 2 pi-periodic functions in the uniform norm parallel to . parallel to C(T) and in the generalized Holder norm parallel to . parallel to omega(beta) where f is an element of H-omega alpha(T) and 0 <= beta < alpha <= 1.