On dual integral equations with Hankel kernel and an arbitrary weight function
In this paper we deal with dual integral equations with an arbitrary weight function and Hankel kernels of distinct and general order. We propose an operational procedure, which depends on exploiting the properties of the Mellin transforms, and readily reduces the dual equations to a single equation...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000364 |
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| _version_ | 1832559155504742400 |
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| author | C. Nasim |
| author_facet | C. Nasim |
| author_sort | C. Nasim |
| collection | DOAJ |
| description | In this paper we deal with dual integral equations with an arbitrary weight function and Hankel kernels of distinct and general order. We propose an operational procedure, which depends on exploiting the properties of the Mellin transforms, and readily reduces the dual equations to a single equation. This then can be inverted by the Hankel inversion to give us an equation of Fredholm type, involving the unknown function. Most of the known results are then derived as special cases of our general result. |
| format | Article |
| id | doaj-art-92524361370e4019b61159c9db5acd8a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-92524361370e4019b61159c9db5acd8a2025-02-03T01:30:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019229330010.1155/S0161171286000364On dual integral equations with Hankel kernel and an arbitrary weight functionC. Nasim0Department of Mathematics and Statistics, The University of Calgary, Calgary T2N 1N4, Alberta, CanadaIn this paper we deal with dual integral equations with an arbitrary weight function and Hankel kernels of distinct and general order. We propose an operational procedure, which depends on exploiting the properties of the Mellin transforms, and readily reduces the dual equations to a single equation. This then can be inverted by the Hankel inversion to give us an equation of Fredholm type, involving the unknown function. Most of the known results are then derived as special cases of our general result.http://dx.doi.org/10.1155/S0161171286000364dual integral equationBessel functions of first kindMellin transformsthe Parseval theorem |
| spellingShingle | C. Nasim On dual integral equations with Hankel kernel and an arbitrary weight function International Journal of Mathematics and Mathematical Sciences dual integral equation Bessel functions of first kind Mellin transforms the Parseval theorem |
| title | On dual integral equations with Hankel kernel and an arbitrary weight function |
| title_full | On dual integral equations with Hankel kernel and an arbitrary weight function |
| title_fullStr | On dual integral equations with Hankel kernel and an arbitrary weight function |
| title_full_unstemmed | On dual integral equations with Hankel kernel and an arbitrary weight function |
| title_short | On dual integral equations with Hankel kernel and an arbitrary weight function |
| title_sort | on dual integral equations with hankel kernel and an arbitrary weight function |
| topic | dual integral equation Bessel functions of first kind Mellin transforms the Parseval theorem |
| url | http://dx.doi.org/10.1155/S0161171286000364 |
| work_keys_str_mv | AT cnasim ondualintegralequationswithhankelkernelandanarbitraryweightfunction |