### Moduli of continuity of functions in Holder’s class by First kind Chebyshev Wavelets and Its Applications in the Solution of Lane-Emden Differential Equations

#### Abstract

In this paper , two new moduli of continuityand two estimators E2k−1,0 and,E2k−1,M of a functions f in H¨older’s class Hα,2ωk [0, 1) by First kind Chebyshev Wavelets have been determined. These moduli of continuity and estimators are new and best possible in wavelet analysis. Applying this technique ,Lane -Emden differential equations have been solved by first kind Chebyshev wavelet method.These solutions obtained by first kind Chebyshev wavelet method are approximately coincided with their exact solutions. This is a significant achievement of this research paper in wavelet analysis.

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R.A.DeVore, "Nonlinear approximation," 1998, Acta Numerica, Cambridge University Press (Cambridge), Vol. 7, pp. 51-150.

L.Debnath, "Wavelet Transform and Their Applications," 2002, Birkhauser, Massachusetts (Boston).

Y.Meyer, "Progress in Wavelet Analysis and Applications," 1993, Frontieres, Gif-sur-Yvette, pp. 9-18.

J.Morlet, G.Arens, E.Fourgeau and D.Giard, "Wave propagation and sampling theory-part II: Sampling theory and complex waves," Geophysics, 1982, Vol. 47(2), pp. 222-236.

E.Babolian, and F. Fattahzadeh, "Numerical Solution of Differential Equations by Using Chebyshev Wavelet Operational Matrix of Integration," Appl. Math. and Comput., 2007, Vol. 188(1), pp. 417-426.

I. Daubechies, "Ten Lectures on Wavelets," 1992, Society for Industrial and Applied Mathematics, Philadelphia (Pennsylvania).

Sharanjeet Dhawan, José A. Tenreir Machado, Dariusz W. Brzeziński and Mohamed S. Osman, "A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems," Symmetry, 2021, Vol. 13(4), pp. 536-549.

A.Zygmund, "Trigonometric Series," 1959, Cambridge University Press, New York, vol. 1(2), p. 115.

C.K.Chui, "An Introduction to Wavelets," 1992, Academic Press, Massachusetts, Vol. 1, p. 41.

A.G. Babenko, Y.V. Kryakin and P.T. Staszak, "Special moduli of continuity and the constant in the jackson-stechkin theorem," Constructive Approximation, 2013, Vol. 38(3), pp. 339-364.

G. Das, T. Ghosh and B. K. Ray, "Degree of approximation of functions by their Fourier series in the generalized Hölder metric," Proc. Indian Acad. Sci. (Math. Sci.), 1996, Vol. 106(2), pp. 139-153.

A.M.Wazwaz, "A new algorithm for solving differential equations of Lane-Emden type," Applied Mathematics and Computation, 2001, Vol. 118(2), pp. 287-310.

M.A. Fariborzi Araghi, S. Daliri, M.Bahmanpour, "Numerical Solution of Integro-Differential Equation by using Chebyshev Wavelet Operational Matrix of Integration," International Journal of Mathematical Modelling & Computations, 2012, Vol. 02(2), pp. 127-136.

B.Sripathy, P.Vijayaraju, G.Hariharan, "Chebyshev Wavelet Based Approximation Method to Some Non-Linear Differential Equations Arising in Engineering," Int. J. of Math. Anal, 2015, vol. 9, pp. 993-1010.

DOI: http://dx.doi.org/10.23755/rm.v47i0.794

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