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 a Volterra integral equations of the second kind with continuous kernel. Normality and continuity of the integral operator are also discussed. Mathematics Subject Classification (2010): 45L05; 46B45; 65R20. Key–Words: Banach space, Volterra–Fredholm integral equation, Separation of variables method. |
