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Some results on generalization $\alpha-$Chebyshev wavelets | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 2 - شماره پیاپی 32، مرداد 2025، صفحه 191-201 اصل مقاله (505.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24101.1702 | ||
| نویسندگان | ||
| Hamid Mazaheri* 1؛ Aabdul Wali Safi1؛ Seayed Mohammad Jesmani2 | ||
| 1Department of Mathematics, Yazd University, 89195-74, Yazd, Iran | ||
| 2Department of Materials and Metallurgical Engineering, National University of Skills(NUS), Tehran, Iran | ||
| چکیده | ||
| In this paper, we introduce generalized formulae for well-known functions such as $\alpha$-Chebyshev functions. We define $\alpha-$Chebyshev wavelets approximation and generalization $\alpha-$wavelet coapproximation. We show that if $\sum_{n=0}^k\sum_{n=0}^{\infty} |t_n|^2L_{n,m}^\alpha$ is convergent, then generalization $\alpha-$Chebyshev wavelets approximation (generalization $\alpha-$ wavelets coapproximation) exists. | ||
| کلیدواژه‌ها | ||
| Generalized $\alpha-$Chebyshev functions؛ Generalized $\alpha-$Chebyshev wavelets approximation؛ Generalized $\alpha-$wavelets coapproximation | ||
| مراجع | ||
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[1] Altnkaya, S., Yalcn, The (p; q)-Chebyshev polynomial bounds of a general bi-univalent function class. Bol. Soc. Mat. Mex. (3) 26 (2020), no. 2, 341{348.
[2] Brandi, Ricci, P. E., Some properties of the pseudo-Chebyshev polynomials of half-integer degree Tbilisi Math. J. 12 (2019), no. 4, 111-121
[3] C akmak, M. Uslu, K. A. generalization of Chebyshev polynomials with well-known kinds and transition relations. Acta Univ. Apulensis Math. Inform. No. 57 (2019), 19-30.
[4] Kumar, L. S., Mishra, S., Awasthi, S. K., Error bounds of a function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet and its applications in the approximation of functions. Carpathian Math. Publ. 14 (2022), no. 1, 29-48.
[5] Nigam, H. K. Mohapatra, R. N. Murari, K. Wavelet approximation of a function using Chebyshev wavelets. Thai J. Math. (2020), 197-208.
[6] Jesmani, S. M., Mazaheri, H. and Shojaeian, S.Wavelet approximation with Chebyshev. Iranian Journal of Numerical Analysis and Optimization. 1 (2024), no. 28, 315-329.
[7] Mason, J. C. Handscomb, D. C. Chebyshev polynomials. Chapman and Hall/CRC, Boca Raton, FL, 2003. | ||
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