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Trigonometric Fourier Approximation of the Conjugate Series of a Function of Generalized Lipchitz Class by Product Summability

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Computational Intelligence in Data Mining—Volume 1

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 410))

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Abstract

Trigonometric Fourier approximation and Lipchitz class of function had been introduced by Zygmund and McFadden respectively. Dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. have established certain theorems. Extending their results, in this paper a theorem on trigonometric approximation of conjugate series of Fourier series of a function \( f \in \,Lip\,\left( {\alpha ,r} \right) \) by product summability (E, s) (N, p n , q n ) has been established.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar, India

    B. P. Padhy

  2. Biswasray Science College, Patapur, Ganjam, Odisha, India

    P. K. Das

  3. Department of Mathematics, B.A. College, Berhampur, Odisha, India

    M. Misra

  4. Department of Mathematics, Berhampur University, Berhampur, Odisha, India

    P. Samanta

  5. National Institute of Scince and Technology, Ganjam, Odisha, India

    U. K. Misra

Authors
  1. B. P. Padhy
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  2. P. K. Das
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  3. M. Misra
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  4. P. Samanta
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  5. U. K. Misra
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Corresponding author

Correspondence to B. P. Padhy .

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Editors and Affiliations

  1. Veer Surendra Sai University of Tech., Dept of Computer Sci Eng & IT, Sambalpur, Odisha, India

    Himansu Sekhar Behera

  2. National Institute of Technology, Dept. of Computer Science & Engineering, Rourkela, Odisha, India

    Durga Prasad Mohapatra

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Padhy, B.P., Das, P.K., Misra, M., Samanta, P., Misra, U.K. (2016). Trigonometric Fourier Approximation of the Conjugate Series of a Function of Generalized Lipchitz Class by Product Summability. In: Behera, H., Mohapatra, D. (eds) Computational Intelligence in Data Mining—Volume 1. Advances in Intelligent Systems and Computing, vol 410. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2734-2_19

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  • DOI: https://doi.org/10.1007/978-81-322-2734-2_19

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2732-8

  • Online ISBN: 978-81-322-2734-2

  • eBook Packages: EngineeringEngineering (R0)

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