Extended Chebyshev Wavelet of First Kind and its Applications in Approximation of a Function Belonging to Hölder’s Class and Solution of Fredholm Integral Equation of Second Kind

Note: Please see pdf for full abstract with equations. In this paper, six approximations E (1) µk , 0, E (1) µk,M , E (2) µk,0 , E (2) µk,M ,E ( 3) µk,0 ,E (3) µk,M of functions of classes H α [0, 1), H α , χ [0, 1), H ϕ [0, 1) by ( µ k , 0) th and ( µ k , M ) th partial sums of their first kind extended Chebyshev wavelet expansion inthe interval [0, 1), for µ > 1, have been estimated. The solution of the Fredholm integral equation of the second kind by the first kind extendedChebyshev wavelets have been obtained. The solution obtained by extended Chebyshev wavelet of the first kind is approximately the same astheir exact solution. This is a significant achievement of this researchpaper in wavelet analysis. Mathematics Subject Classification 42C40, 45B05, 65T60, 65R20.