A Functional Equation of Aczél and Chung in Generalized Functions

Jae-Young Chung Department of Mathematics, Kunsan National University, Kunsan 573-701, South Korea Correspondence should be addressed to Jae-Young Chung, [email protected] Received 1 October 2008; Revised 22 December 2008; Accepted 25 December 2008 Recommended by Patricia J. Y. Wong 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. Copyright q 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.