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Ass. Lect. Mohamed Abdallah Abdel-Aty Ali :: Publications:

Analytical discussion for the mixed integral equations
Authors: M. E. Nasr; M. A. Abdel-Aty
Year: 2018
Keywords: Banach space; Volterra–Fredholm integral equation; degenerate kernel method.
Journal: Journal of Fixed Point Theory and Applications
Volume: 20
Issue: 3
Pages: Not Available
Publisher: Springer International Publishing AG, part of Springer Nature 2018
Local/International: International
Paper Link:
Full paper Not Available
Supplementary materials Not Available

This paper presents a numerical method for the solution of a Volterra–Fredholm integral equation in a Banach space. Banachs fixed point theorem is used to prove the existence and uniqueness of the solution. To find the numerical solution, the integral equation is reduced to a system of linear Fredholm integral equations, which is then solved numerically using the degenerate kernel method. Normality and continuity of the integral operator are also discussed. The numerical examples in Sect. 5 illustrate the applicability of the theoretical results.

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