On a discussion of Volterra–Fredholm integral equation with discontinuous kernel
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 probl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-02-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s42787-020-00074-8 |
| Summary: | 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. |
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| ISSN: | 2090-9128 |