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Degree of approximation of functions belonging to \(Lip(\omega (t),p)\)-class by linear operators based on Fourier series

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Abstract

Fourier series and operators based on it are of great importance in both theoretical and applied mathematics because they can be considered as representation of a function or signal. In this paper, we estimate the degree of approximation of \(f \in Lip(\omega (t),p)\)-class and its conjugate \(\tilde{f},\) by matrix means of their trigonometric Fourier series by relaxing the conditions on \(\omega (t)\) imposed by the earlier researchers. We also discuss some results which are analogous to our results.

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References

  1. Zygmund, A.: Trigonometric series, 3rd edn. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  2. Srivastava, S.K., Singh, U.: Trigonometric approximation of periodic functions belonging to \(Lip(\omega (t), p)\) -class. J. Comput. Appl. Math. 270, 223–230 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Khan, H.H., Ram, G.: On the degree of approximation. Facta Univ. Ser. Math. Inform. 18, 47–57 (2003)

    MathSciNet  MATH  Google Scholar 

  4. Zhang, R.: A note on the trigonometric approximation of \(Lip(\omega (t), p)\)-class. Appl. Math. Comput. 269, 129–132 (2015)

    MathSciNet  Google Scholar 

  5. Rhoades, B.E.: The degree of approximation of functions, and their conjugates belonging to several general Lipschitz classes by Hausdorff matrix means of the Fourier series and conjugate series of a Fourier series. Tamkang J. Math. 45, 389–395 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lal, S., Mishra, A.: Euler-Hausdorff matrix summability operator and trigonometric approximation of the conjugate of a function belonging to the generalized Lipschitz class. J. Inequal. Appl. 2013, 59 (2013)

  7. McFadden, L.: Absolute Nörlund summability. Duke Math. J. 9, 168–207 (1942)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This research is supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India in the form of fellowship to the first author.

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Authors and Affiliations

  1. Department of Mathematics, IIT Roorkee, Roorkee, 247667, Uttarakhand, India

    Soshal Saini & Uaday Singh

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  1. Soshal Saini
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  2. Uaday Singh
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Correspondence to Soshal Saini.

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Saini, S., Singh, U. Degree of approximation of functions belonging to \(Lip(\omega (t),p)\)-class by linear operators based on Fourier series. Boll Unione Mat Ital 9, 495–504 (2016). https://doi.org/10.1007/s40574-016-0064-2

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  • DOI: https://doi.org/10.1007/s40574-016-0064-2

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