Demonstratio Mathematica (Oct 2019)

On approximation in generalized Zygmund class

  • Nigam Hare Krishna

DOI
https://doi.org/10.1515/dema-2019-0022
Journal volume & issue
Vol. 52, no. 1
pp. 370 – 387

Abstract

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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.

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