On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series.

*(English)*Zbl 1213.42007Summary: In a recent paper S. Lal and 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 the Lipschitz class Lip\(\alpha \) using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions.

##### MSC:

42A10 | Trigonometric approximation |

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\textit{B. E. Rhoades} et al., Appl. Math. Comput. 217, No. 16, 6868--6871 (2011; Zbl 1213.42007)

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##### References:

[1] | Lal, Shyam, On degree of approximation of functions belonging to the weighted (Lp,ξ(t)) class by (C,1)(E,1) means, Tamkang J. math., 30, 47-52, (1999) · Zbl 1032.42004 |

[2] | Lal, Shyam, On degree of approximation of functions belonging to the weighted W(lp,ξ(t)) class by matrix summability means of conjugate series of a Fourier series, Tamkang J. math., 31, 279-288, (2000) · Zbl 1032.42005 |

[3] | Lal, Shyam; Singh, Prem Narain, On approximation of (Lp,ξ(t)) function by (C,1)(H,1) means of its Fourier series, Indian J. pure appl. math., 33, 1443-1449, (2002) · Zbl 1085.42501 |

[4] | Lal, S.; Yadov, K.N.S., On degree of approximation of function belonging to the Lipschitz class by means (C,1)(H,1) of its Fourier series, Bull. Calcutta math. soc., 93, 191-196, (2001) · Zbl 1032.42003 |

[5] | Qureshi, L., On the degree of approximation of functions belonging to the weighted W(lp,ξ(t)) class, Tamkang J. math., 13, 471-475, (1982) · Zbl 0492.42004 |

[6] | Rhoades, B.E., On the degree of approximation of functions belonging to the weighted (Lp,ξ(t)) class by Hausdorff means, Tamkang J. math., 32, 305-314, (2001) · Zbl 0999.42005 |

[7] | Zygmund, A., Trigonometric series, (1968), Cambridge University Press Cambridge · JFM 58.0296.09 |

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