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On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series. (English) Zbl 1039.42001
Summary: In a recent paper, {\it S. Lal} and {\it K. N. S. Yadav} [Bull. Calcutta Math. Soc. 93, No. 3, 191--196 (2001; Zbl 1032.42003)] obtained a theorem on the degree of approximation for a function belonging to a Lipschitz class using a triangular matrix transform of the Fourier series representation of the function. The matrix involved was the product of $(C,1)$, the Cesàro matrix of order one, with $(E,1)$, the Euler matrix of order one. In this paper we extend this result to a much wider class of Hausdorff matrices.
42A10Trigonometric approximation
42A24Summability and absolute summability of Fourier and trigonometric series
40C05Matrix methods in summability