On a discussion of Volterra–Fredholm integral equation with discontinuous kernel

Abstract

Abstract The purpose of this paper is to establish the general solution of a Volterra–Fredholm integral equation with discontinuous kernel in a Banach space. Banach’s fixed point theorem is used to prove the existence and uniqueness of the solution. By using separation of variables method, the problem is reduced to Volterra integral equations of the second kind with continuous kernel. Normality and continuity of the integral operator are also discussed.

Keywords

• Banach space
• Volterra–Fredholm integral equation
• Separation of variables method