IJPAM: Volume 63, No. 4 (2010)

ORTHOGONAL STABILITY OF 2 DIMENSIONAL MIXED
TYPE ADDITIVE AND QUARTIC FUNCTIONAL EQUATION

M. Arunkumar$^1$, S. Hema Latha$^2$
$^1$Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Tamil Nadu, INDIA
e-mail: [email protected]
$^2$Department of Mathematics
Annai Veilankanni's College of Arts and Science
Saidapet, Chennai, 600 015, Tamil Nadu, INDIA
e-mail: [email protected]


Abstract.In this paper, the authors investigate the orthogonal stability of 2 dimensional mixed type additive and quartic functional equation of the form
\begin{multline*}
7[f(2x+y)+f(2x-y)]\\
= 28[f(x+y)+f(x-y)]-3[f(2y)-2f(y)]+14[f(2x)-4f(x)],
\end{multline*}
with $x \perp y$, where $\perp$ is orthogonality in the sense of Ratz.

Received: May 8, 2010

AMS Subject Classification: 39B55, 39B52, 39B82, 46H25

Key Words and Phrases: Hyers-Ulam-Aoki-Rassias stability, Ulam-Gavruta-Rassias stability, J.M. Rassias stability, additive functional equation, quartic functional equation, orthogonality space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 4