Advances in Difference Equations
Volume 2008 (2008), Article ID 147979, 11 pages
doi:10.1155/2008/147979
Research Article
A Functional Equation of Aczél and Chung in Generalized Functions
Department of Mathematics, Kunsan National University, Kunsan 573-701, South Korea
Received 1 October 2008; Revised 22 December 2008; Accepted 25 December 2008
Academic Editor: Patricia J. Y. Wong
Copyright © 2008 Jae-Young Chung. 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 consider an n-dimensional version of the functional equations of Aczél and Chung in the spaces of generalized functions such as the Schwartz distributions and Gelfand generalized functions. As a result, we prove that the solutions of the distributional version of the equation coincide with those of classical functional equation.