Some results on generalization $\alpha-$Chebyshev wavelets

Document Type : Research Paper

Authors

1 Department of Mathematics, Yazd University, 89195-74, Yazd, Iran

2 Department of Materials and Metallurgical Engineering, National University of Skills(NUS), Tehran, Iran

Abstract

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.

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Articles in Press, Accepted Manuscript
Available Online from 20 February 2025
  • Receive Date: 29 September 2024
  • Revise Date: 06 December 2024
  • Accept Date: 19 February 2025