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

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 red...

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Bibliographic Details
Published in:	Journal of the Egyptian Mathematical Society Vol. 28; no. 1; pp. 1 - 10
Main Authors:	Abdou, M. A., Soliman, A. A., Abdel–Aty, M. A.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 28-02-2020 Springer Nature B.V SpringerOpen
Subjects:	Applied mathematics Banach space Banach spaces Inequality Integral equations Mathematics Mathematics and Statistics Original Research Physics Separation of variables method Volterra–Fredholm integral equation secondary 65R20 Volterra–Fredholm integral equation 45L05 Primary 46B45 Banach space Separation of variables method
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Summary:	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.
ISSN:	2090-9128 1110-256X 2090-9128
DOI:	10.1186/s42787-020-00074-8