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Approximation of a Function f Belonging to Generalized Hölder Class of Order 0 < α ≤ 1 and Generalized Lipschitz class by Haar Wavelet Method

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Abstract

In this paper, the approximations of a function f of generalized Hölder class \(H^{(w)}_{\alpha }[0,1]\) and generalized Lipschitz class \(Lip^{(s)}_{\alpha }[0,1]\) have been obtained by Haar wavelet method. Calculated approximations are best possible in wavelet analysis.

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References

  1. Gesztesy F, Godefroy G, Grafakos L, Verbitsky I (eds) (2016) Spaces of Lipschitz and Hölder functions and their applications. In: Nigel J. Kalton Selecta. Contemporary mathematicians. vol 2, pp 325–376. Birkhäuser, Cham

  2. Titchmarsh EC (1939) The theory of functions, 2nd edn. Oxford University Press, Oxford

    MATH  Google Scholar 

  3. Abbas Z, Vahdati S, Kajani MT, Atan KA (2009) New construction of wavelets base on floor function. Appl Math Comput 210(2):473–478

    MathSciNet  MATH  Google Scholar 

  4. Chui CK (1992) An introduction to wavelets (Wavelet analysis and its applications), vol 1. Academic Press, Cambridge

    Google Scholar 

  5. Wojtaszczyk P (1997) A mathematical introduction to wavelets, vol 37. Cambridge University Press, Cambridge

    Book  Google Scholar 

  6. Zygmund A (1959) Trigonometric series, vol I. Cambridge University Press, Cambridge

    MATH  Google Scholar 

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Correspondence to Shyam Lal.

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Lal, S., Sharma, V.K. Approximation of a Function f Belonging to Generalized Hölder Class of Order 0 < α ≤ 1 and Generalized Lipschitz class by Haar Wavelet Method. Natl. Acad. Sci. Lett. 43, 271–275 (2020). https://doi.org/10.1007/s40009-019-00835-9

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  • DOI: https://doi.org/10.1007/s40009-019-00835-9

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