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Bull. Korean Math. Soc. 2009; 46(2): 295-301
Printed March 1, 2009
https://doi.org/10.4134/BKMS.2009.46.2.295
Copyright © The Korean Mathematical Society.
On a stability of Pexiderized exponential equation
Jaeyoung Chung
Kunsan National University
We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings $f, g, h:G\times S\rightarrow\mathbb{C}$, where $G$ is an abelian group and $S$ is a commutative semigroup which is divisible by $2$. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.
Keywords: distribution, Sato hyperfunction, Fourier hyperfunction, Pexiderized exponential equation, heat kernel, stability
MSC numbers: 39B82, 46F15
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