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Abstract and Applied Analysis
Volume 2013, Article ID 539240, 6 pages
http://dx.doi.org/10.1155/2013/539240
Research Article

On Modified Mellin Transform of Generalized Functions

1Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan
2Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 10 September 2013; Accepted 14 November 2013

Academic Editor: S. A. Mohiuddine

Copyright © 2013 S. K. Q. Al-Omari and Adem Kılıçman. 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 investigate the modified Mellin transform on certain function space of generalized functions. We first obtain the convolution theorem for the classical and distributional modified Mellin transform. Then we describe the domain and range spaces where the extended modified transform is well defined. Consistency, convolution, analyticity, continuity, and sufficient theorems for the proposed transform have been established. An inversion formula is also obtained and many properties are given.