IJPAM: Volume 36, No. 3 (2007)

STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

K. Ravi$^1$, M. Arun Kumar$^2$
$^{1,2}$Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Tamil Nadu, INDIA
$^1$e-mail: shckravi@yahoo.co.in
$^2$e-mail: annarun2002@gmail.com


Abstract.In this paper, the authors investigate the generalized Hyers-Ulam-Rassias stability and Ulam-Gavruta-Rassias stability of a new quadratic functional equation
\begin{multline*} f(x+y+z)+f(x+y-z)+f(x-y+z)\\ = f(x+y)+ f(x+z)+f(y-z)+f(x)+f(y)+f(z). \end{multline*}
The Hyers-Ulam stability of this equation on bounded domain is also discussed.

Received: February 17, 2007

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

Key Words and Phrases: quadratic functional equation, Hyers-Ulam-Rassias stability, Ulam-Gavruta-Rassias stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3