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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 2, Pages 293-300

On dual integral equations with Hankel kernel and an arbitrary weight function

Department of Mathematics and Statistics, The University of Calgary, Calgary T2N 1N4, Alberta, Canada

Received 3 July 1985

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.