Special version of the subdomain method for a class of integral equations of the third kind in the space of distributions

Abstract

In this paper we suggest and substantiate special direct methods for finding approximate solutions to integral equations of the third kind in the space of distributions. We consider a general case of location of zeroes of a coefficient. The method is based on using the Kantorovich polynomials.Keywords: integral equation of the third kind, space of distributions, approximate solution, theoretical substantiation, subdomain method. Spaces of finite functions and distributions.Let C ≡ C(I) be the space of continuous on I functions with the max-norm. According to [12], we say that a function y ∈ C belongs to the class C{m; t 0 } if there exists the Taylor derivative y {m} (t 0 ) of order m at the point t 0 ∈ (0, 1) . *