Open Access Research

Stability of quadratic functional equations in tempered distributions

Young-Su Lee

Author Affiliations

Department of Mathematics, Sogang University, Seoul, 121-741, Republic of Korea

Journal of Inequalities and Applications 2012, 2012:177 doi:10.1186/1029-242X-2012-177

Published: 16 August 2012

Abstract

We reformulate the following quadratic functional equation:

<a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/177/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/177/mathml/M1">View MathML</a>

as the equation for generalized functions. Using the fundamental solution of the heat equation, we solve the general solution of this equation and prove the Hyers-Ulam stability in the spaces of tempered distributions and Fourier hyperfunctions.

Keywords:
quadratic functional equation; stability; tempered distribution; heat kernel; Gauss transform