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Here, we estimate the degree of approximation of a conjugate function g˜{\tilde g} and a derived conjugate function g˜′{\tilde g'} , of a 2π-periodic function g∈Zrλg \in Z_r^\lambda , r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.

Abstract In the present work, a best approximation of a function f in Besov space using the generalized Nörlund–Hausdorff (Npq△H) $(N_{pq}\triangle _{H})$ product means, for the two different cases 1

Abstract In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class Z p ( ω ) $Z_{p}^{(\omega)}$ ( p ≥ 1 $p \ge1$ ) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.