Approximation in the Zygmund class

Approximation of functions in the generalized Zygmund class using Hausdorff means

In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class [Formula: see text] ([Formula: see text]) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.

On the Maximum Value for Zygmund Class on an Interval

Best Approximation of Functions of Generalized Zygmund Class by Matrix-euler Summability Means of Fourier Series (communicated by Hüsein Bor)

The degree of approximation of a function f belonging to Lipschitz class by the Cesàro mean and f ∈ Hα by the Fejér means has been studied by Alexits [4] and Prössdorf [7] respectively. But till now no work seems to have been done to obtain best approximation of functions belonging to generalized Zygmund class, Z (w) r , (r ≥ 1) by product summability means of the form (∆.E1). Z (w) r class is ...

Voronovskaja’s theorem and the exact degree of approximation for the derivatives of complex Riesz-Zygmund means

In this paper we obtain a quantitative Voronovskaja result and the exact orders in approximation by the derivatives of complex Riesz-Zygmund means in compact disks. 2000 Mathematical Subject Classification: Primary : 30E10 ; Secondary : 41A25, 41A28.

The Zygmund Morse-sard Theorem

The classical Morse-Sard Theorem says that the set of critical values of f : R → R has Lebesgue measure zero if f ∈ Ck+1. We show the Ck+1 smoothness requirement can be weakened to Ck+Zygmund. This is corollary to the following theorem: For integers n > m > r > 0, let s = (n− r)/(m− r); if f : R → R belongs to the Lipschitz class Λs and E is a set of rank r for f , then f(E) has measure zero. 0...