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In this paper, first and second kind Chebyshev wavelets are studied. New estimators    $$E_{2^{k-1},0}^{(1)}$$  E 2 k - 1 , 0 ( 1 ) ,    $$E_{2^{k-1},M}^{(2)}$$  E 2 k - 1 , M ( 2 ) ,    $$E_{2^{k-1},0}^{(3)}$$  E 2 k - 1 , 0 ( 3 ) ,    $$E_{2^{k-1},M}^{(4)}$$  E 2 k - 1 , M ( 4 ) for first kind Chebyshev wavelets and estimators    $$E_{2^{k},0}^{(5)}$$  E 2 k , 0 ( 5 ) ,    $$E_{2^{k},M}^{(6)}$$  E 2 k , M ( 6 ) ,    $$E_{2^{k},0}^{(7)}$$  E 2 k , 0 ( 7 ) and    $$E_{2^{k},M}^{(8)}$$  E 2 k , M ( 8 ) for second kind Chebyshev wavelets for a function  f  belonging to generalized H   $$\ddot{o}$$  o ¨ lder’s class have been obtained. Also, a method based on first and second kind Chebyshev wavelet approximations has been presented for solving integral equations. Comparison of solutions obtained by both wavelets method has been studied. It is found that second kind Chebyshev wavelet method gives better and accurate solutions as compared to first kind Chebyshev wavelet method. This is a significant achievement of this research paper in wavelet analysis.

arabian journal of mathematics

Approximation of function belonging to generalized Hölder’s class by first and second kind Chebyshev wavelets and their applications in the solutions of Abel’s integral equations