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.

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In this paper, the existence and uniqueness solution of the Fredholm-Volterra integral equations (F-VIEs) are considered in the space L 2 [0, 1]× C n [0, T ], 0 ≤ T < 1. Using a numerical technique, F-VIEs lead to a system of linear Fredholm integral equations (SLFIEs). Also, the normality and the continuity of integral operator are discussed. The Trapezoidal Rule is used to get the solution of SLFIEs. Finally, numerical results are discussed and the error estimate is computed.