Constructive method for solvability of Fredholm equation of the first kind

Abstract

The solvability and construction of the general solution of the first kind Fredholm integral equation are among the insufficiently explored problems in mathematics. There are various approaches to solve this problem. We note the following methods for solving of ill-posed problem: regularization method, the method of successive approximations, the method of undetermined coefficients. The purpose of this work is to create a new method for solvability and construction of solution of the integral equation of the first kind. As it follows from the foregoing, the study of the solvability and construction of a solution of the Fredholm integral equation of the first kind is topical. A new method for studying of solvability and construction of a solution for Fredholm integral equation of the first kind is proposed. Solvability conditions and the construction method of an approximate solution of the integral Fredholm equation of the first kind are obtained.

Keywords

• integral equation
• solvability
• construction of a solution
• extreme problem
• functional gradient
• minimizing sequences