Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 608712, 10 pages
http://dx.doi.org/10.5402/2012/608712
Research Article

New Inversion Techniques for Some Integral Transforms via the Generalized Product Theorem of the Mellin Transform

Department of Mathematics, Faculty of Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

Received 21 December 2011; Accepted 17 January 2012

Academic Editors: C. Chen, F. Ding, and H. Homeier

Copyright © 2012 Alireza Ansari and Mohammadreza Ahmadi Darani. 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.

Abstract

We introduce the generalized product theorem for the Mellin transform, and we solve certain classes of singular integral equations with kernels coincided with conditions of this theorem. Also, new inversion techniques for the Wright, Mittag-Leffler, Stieltjes, and Widder potential transforms are obtained.