On the Existence of Approximate Solution of Fredholm Integral Equation of the First Kind by Band-Limited Scaling Function

In this paper, we study the existence and uniqueness of the solution of Fredholm integral equation of the first kind with convolution type kernel. These results are based on band-limited scaling function which is generated by a class of band-limited wavelets. Since these band-limited functions are infinitely differentiable and possess rapid decay property, methods based on these functions would be highly accurate. Finally, convergence analysis has been discussed to validate the approximate solution.