APPROXIMATION OF CONTIONUOUS FUNCTIONS BY VALLEE-POUSSIN’S SUMS

Abstract

Let \(V_{n,m}^{(α,β)}(f;x)\)= \(\frac{1}{m+1}\) \(\displaystyle \sum_{k=n}^{n+m} S_{k}^{(α,β)}(f;x)\) be the Vallee-Poussin’s partial sums of Fourier-Jacobi series.  In this paper, we study the deviations of \(V_{n,m}^{(α,β)}(f;x)\) on [−1, 1] for continuous function f(x).