Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 1999; 14(1): 75-80

Printed March 1, 1999

Copyright © The Korean Mathematical Society.

On the Superstability of the Functional Equation $f(x_1+\dots+x_m)=f(x_1)\dots f(x_m)$

Soon-Mo Jung

Hong--Ik University

Abstract

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First, we shall improve the superstability result of the exponential equation $f(x+y)=f(x)f(y)$ which was obtained in~[4]. Furthermore, the superstability problems of the functional equation $f(x_{1} + \cdots + x_{m}) = f(x_{1}) \cdots f(x_{m})$ shall be investigated in the special settings~(2) and~(9).

Keywords: superstability, exponential equation, Hyers--Ulam--Rassias stability

MSC numbers: Primary 39B72

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