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

Abstract

In this paper, six approximations of solution functions of the Fredholm integral equation in Hölder’s class by first kind extended Chebyshev wavelet expansion in the interval [0, 1) have been estimated. The solutions of the Fredholm integral equation of the second kind by extended Chebyshev wavelets of the first kind have been obtained. The solutions obtained by an extended Chebyshev wavelet of the first kind are approximately the same as their exact solutions. This is a significant achievement of this research paper in wavelet analysis. © Indian Mathematical Society, 2024.