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Bull. Korean Math. Soc. 2009; 46(2): 235-243

Printed March 1, 2009

https://doi.org/10.4134/BKMS.2009.46.2.235

Copyright © The Korean Mathematical Society.

Notes on the superstability of d'Alembert type functional equations

Peng Cao and Bing Xu

Sichuan University

Abstract

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In this paper we will investigate the superstability of the generalized d'Alembert type functional equations $\sum_{i=1}^{m}f(x+\sigma^{i}(y))=kg(x)f(y)$ and $\sum_{i=1}^{m}f(x+\sigma^{i}(y))=kf(x)g(y)$.

Keywords: d'Alembert functional equation, superstability, cosine function

MSC numbers: 39B82, 39B32

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