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.
References
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
Titchmarsh EC (1939) The theory of functions, 2nd edn. Oxford University Press, Oxford
Abbas Z, Vahdati S, Kajani MT, Atan KA (2009) New construction of wavelets base on floor function. Appl Math Comput 210(2):473–478
Chui CK (1992) An introduction to wavelets (Wavelet analysis and its applications), vol 1. Academic Press, Cambridge
Wojtaszczyk P (1997) A mathematical introduction to wavelets, vol 37. Cambridge University Press, Cambridge
Zygmund A (1959) Trigonometric series, vol I. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40009-019-00835-9
Keywords
- \(H^{(w)}_{\alpha }[0, 1]\) class
- \(Lip^{(s)}_{\alpha }[0, 1]\) class
- Haar wavelet
- Wavelet approximation