On a discussion of Volterra–Fredholm integral equation with discontinuous kernel
Abdou, M., Soliman, A., Abdel–Aty, M. (2020). On a discussion of Volterra–Fredholm integral equation with discontinuous kernel. EKB Journal Management System, 28(1), 1-10. doi: 10.1186/s42787-020-00074-8
M. A. Abdou; A. A. Soliman; M. A. Abdel–Aty. "On a discussion of Volterra–Fredholm integral equation with discontinuous kernel". EKB Journal Management System, 28, 1, 2020, 1-10. doi: 10.1186/s42787-020-00074-8
Abdou, M., Soliman, A., Abdel–Aty, M. (2020). 'On a discussion of Volterra–Fredholm integral equation with discontinuous kernel', EKB Journal Management System, 28(1), pp. 1-10. doi: 10.1186/s42787-020-00074-8
Abdou, M., Soliman, A., Abdel–Aty, M. On a discussion of Volterra–Fredholm integral equation with discontinuous kernel. EKB Journal Management System, 2020; 28(1): 1-10. doi: 10.1186/s42787-020-00074-8

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

Journal of the Egyptian Mathematical Society
Volume 28, Issue 1, June 2020, Pages 1-10    PDF (381.05 K)
DOI: 10.1186/s42787-020-00074-8
Authors
M. A. Abdou; A. A. Soliman; M. A. Abdel–Aty
Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt
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
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