solving integral equations of the third kind in the reproducing kernel space

a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical examples are studied to demonstrate the accuracy of the present method. results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.