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.

中文翻译：

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带不连续核的Volterra-Fredholm积分方程的讨论

本文的目的是在 Banach 空间中建立具有不连续核的 Volterra-Fredholm 积分方程的通解。Banach不动点定理用于证明解的存在唯一性。利用变量分离法将问题简化为具有连续核的第二类Volterra积分方程。还讨论了积分算子的正态性和连续性。