Wavelet approximation with Chebyshev wavelets

Document Type : Research Article


1 Department of Materials and Metallurgical Engineering, Technical and Vocational University(TVU), Tehran, Iran.

2 Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.

3 Department of Mathematics, Yazd University, 89195-741, Yazd, Iran


In this paper, we study wavelet approximation of the Chebyshev polyno-mials of the first, second, third, and fourth kinds. We estimate the wavelet approximation of a function f having bounded first derivatives.


Main Subjects

[1] Çakmak, M. and Uslu, K.A. generalization of Chebyshev polynomials with well-known kinds and transition relations, Acta Univ. Apulensis Math. Inform. 57 (2019), 19–30.
[2] Dehghan, M. and Eslahchi, M.R. Best uniform polynomial approxima-tion of some rational functions, Comput. Math. Appl. 59(1) (2010), 382–390.
[3] Eslahchi, M.R. and Dehghan, M. The best uniform polynomial approxi-mation to the class of the form 1 (a2±x2) , Nonlinear Anal. 71(3-4) (2009), 740–750.
[4] Mason, J.C. and Handscomb, D.C. Chebyshev polynomials, Chapman and Hall/CRC, Boca Raton, FL, 2003.
[5] Nigam, H.K., Mohapatra, R.N. and Murari, K. Wavelet approximation of a function using Chebyshev wavelets, Thai J. Math. (2020), 197–208.
[6] Rivlin, T.J. An introduction to the approximation of functions, Corrected reprint of the original. Dover Books on Advanced Mathematics. Dover Publications, Inc., New York, 1981.