Approximation of functions belonging to the generalized Lipschitz class by $C^{1}\cdot N_{p}$ summability method of conjugate series of Fourier series

Vishnu Narayan Mishra; Kejal Khatri; Lakshmi Narayan Mishra

Authors

Vishnu Narayan Mishra Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat-395 007 (Gujarat), India Author
Kejal Khatri Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat-395 007 (Gujarat), India Author
Lakshmi Narayan Mishra L. 1627 Awadh Puri Colony Beniganj, Phase - III, Opp. I.T.I. Ayodhya Main Road, Faizabad - 224 001 (Uttar Pradesh), India Author

Keywords:

Generalized Lipschitz

W (L_{r}, ξ (t))

-class of functions, conjugate Fourier series, degree of approximation,

C^{1}

means,

N_{p}

means, product summability

C^{1} \cdot N_{p}

transform

Subjects:

40G05, 42B05, 42B08

Abstract

In the present study, a new theorem on the degree ofapproximation of function $\tilde{f}$ , conjugate to a periodicfunction $f$ belonging to weighted $W (L_{r}, ξ (t))$ -class usingsemi-monotonicity on the generating sequence ${p_{n}}$ has been established.

Approximation of functions belonging to the generalized Lipschitz class by $C^{1} \cdot N_{p}$ summability method of conjugate series of Fourier series

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Approximation of functions belonging to the generalized Lipschitz class by C1⋅Np summability method of conjugate series of Fourier series

Authors

Keywords:

Subjects:

Abstract

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Published

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Approximation of functions belonging to the generalized Lipschitz class by $C^{1} \cdot N_{p}$ summability method of conjugate series of Fourier series