Modified Hyers-Ulam-Rassias stability of functional equations with square-symmetric operation
Commun. Korean Math. Soc. 2001 Vol. 16, No. 2, 211-223
Gwang Hui Kim, Young Whan Lee, Kyoung Sihn Ji
Kangnam University, Taejon University, Taejon University
Abstract : In this paper, we obtain the modified Hyers-Ulam-Rassias stability for the family of the functional equation $f(x\circ y)$ $=H\big(f(x)^{1/t}$, $f(y)^{1/t}\big)$ $(x,y \in S)$, where $H$ is a homogeneous function of degree $t$ and $\circ$ is a square-symmetric operation on the set $S$.
Keywords : functional equation, homogeneous function, Hyers-Ulam stability, (modified) Hyers-Ulam-Rassias stability
MSC numbers : 39B52, 39B72, 39B82
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