IJPAM: Volume 34, No. 2 (2007)

HYERS-ULAM-RASSIAS STABILITY OF
A QUARTIC FUNCTIONAL EQUATION

K. Ravi$^{1}$, M. Arun Kumar$^{2}$
$^{1,2}$Department of Mathematics
Sacred Heart College
Tirupattur, TamilNadu, 635 601, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability of a quartic functional equation

\begin{displaymath} f(x+2y) + f(x-2y)= 2f(x)+ 32f(y) + 48 f( \sqrt{xy}~ )\,, \end{displaymath}

for all $x,y \in \mathbb{R}$ with the help of Fréchet functional equation.

Received: November 1, 2006

AMS Subject Classification: 39B22, 39B52, 39B72

Key Words and Phrases: difference operator, Fréchet functional equation, $m-$additive function, quartic functional equation, Hyers-Ulam-Rassias stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 2