IJPAM: Volume 104, No. 3 (2015)

HYERS-ULAM-RASSIAS STABILITY OF LIE
$*$-DERIVATIONS OF A CUBIC FUNCTIONAL
EQUATION WITH THREE VARIABLES

Ick-Soon Chang$^1$, Hwan-Yong Shin$^2$
$^{1,2}$Department of Mathematics
Chungnam National University
99 Daehangno, Yuseong-gu, Daejeon 305-764, KOREA


Abstract. We will prove the general solution of the following cubic functional equation
\begin{multline*} 4\{f(2x+y+z)+f(x+2y+z)+f(x+y+2z)\} = 27f(x+y+z)\\ +f(-x+y+z)+f(x-y+z)+f(x+y-z)+12\{f(x)+f(y)+f(z)\} \end{multline*}
and investigate the stability of a cubic Lie $*$-derivation associated with the given functional equation.

Received: March 17, 2015

AMS Subject Classification: 39B82, 39B62

Key Words and Phrases: cubic functional equation, Lie $*$-derivation

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DOI: 10.12732/ijpam.v104i3.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 3
Pages: 299 - 311


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