Abstract
In this paper, we review the previous work done on the degree of approximation of f˜, conjugate of a 2π-periodic function f belonging to the weighted W(Lp,ξ(t))-class and its subclasses such as Lip(ξ(t),p),Lip(α,p)andLipα, and determine the degree of approximation of f˜ by using Hausdorff means of conjugate Fourier series of f. Since (C,1), the Cesàro matrix of order 1, and (E,q), the Euler matrix of order q>0, are Hausdorff matrices, and the product of two Hausdorff matrices is also a Hausdorff matrix [B.E. Rhoades, N.K. Sharma, Spectral results for some Hausdorff matrices, Acta Sci. Math. 44 (1982) 359–364, p. 360, Theorem 1], our theorems generalize and improve some of the previous results. Some corollaries have also been deduced from our results.
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