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.
Abdou, M., Soliman, A., & Abdel–Aty, M. (2020). On a discussion of Volterra–Fredholm integral equation with discontinuous kernel. Journal of the Egyptian Mathematical Society, 28(1), 1-10. doi: 10.1186/s42787-020-00074-8
MLA
M. A. Abdou; A. A. Soliman; M. A. Abdel–Aty. "On a discussion of Volterra–Fredholm integral equation with discontinuous kernel", Journal of the Egyptian Mathematical Society, 28, 1, 2020, 1-10. doi: 10.1186/s42787-020-00074-8
HARVARD
Abdou, M., Soliman, A., Abdel–Aty, M. (2020). 'On a discussion of Volterra–Fredholm integral equation with discontinuous kernel', Journal of the Egyptian Mathematical Society, 28(1), pp. 1-10. doi: 10.1186/s42787-020-00074-8
VANCOUVER
Abdou, M., Soliman, A., Abdel–Aty, M. On a discussion of Volterra–Fredholm integral equation with discontinuous kernel. Journal of the Egyptian Mathematical Society, 2020; 28(1): 1-10. doi: 10.1186/s42787-020-00074-8
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