Abstract
In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class Z_{p}^{(omega)} (p ge1) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.
Highlights
During the last few decades the degree of approximation of functions belonging to various Lipschitz classes (Lip α, Lip(α, p), Lip(ξ (t), p), W (Lp, ξ (t)) etc.) has been studied by various investigators using different summability methods such as Cesàro, Hölder, Euler and their products
Multiplication of two Hausdorff matrices is commutative. In view of these remarks, Rhoades [ – ], Singh, Srivastava [ ] have obtained the degree of approximation of functions belonging to various Lipschitz classes using Hausdorff means
In this paper we prove two theorems on approximation of a function by Hausdorff means of its Fourier series in terms of Zygmund modulus of continuity
Summary
During the last few decades the degree of approximation of functions belonging to various Lipschitz classes (Lip α, Lip(α, p), Lip(ξ (t), p), W (Lp, ξ (t)) etc.) has been studied by various investigators (see [ – ] and the references therein) using different summability methods such as Cesàro, Hölder, Euler and their products. In view of these remarks, Rhoades [ – ], Singh, Srivastava [ ] have obtained the degree of approximation of functions belonging to various Lipschitz classes using Hausdorff means. To the best of our knowledge, the approximation of functions belonging to the generalized Zygmund class by Hausdorff means has not been investigated so far. This motivated us to work in this direction.
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