IJPAM: Volume 54, No. 1 (2009)

STABILITY OF CUBIC AND ADDITIVE
FUNCTIONAL EQUATION IN QUASI-BANACH SPACES

K. Ravi$^1$, R. Kodandan$^2$, P. Narasimman$^3$
$^1$Department of Mathematics
Sacred Heart College
Tirupattur, 635 601, Tamil Nadu, INDIA
e-mail: [email protected]
$^2$Department of Mathematics
Srinivasa Institute of Technology and Management Studies
Chittoor, 517 127, Andhra Pradesh, INDIA
e-mail: [email protected]
$^3$Department of Mathematics
Priyadarshini Engineering College
Vaniyambadi, 635 751, Tamil Nadu, INDIA
e-mail: [email protected]


Abstract.In this paper, we introduce and investigate the general solution of a new cubic and additive functional equation
\begin{multline*}
3f(x+y+z)+f(-x+y+z)+f(x-y+z)+f(x+y-z)+4[f(x)+f(y)+f(z)]\\
=4[f(x+y)+f(x+z)+f(y+z)]
\end{multline*}
and discuss its Hyers-Ulam-Rassias and J.M. Rassias stability in quasi-Banach spaces.

Received: June 10, 2009

AMS Subject Classification: 39B52, 39B82, 39B72, 46B03

Key Words and Phrases: Hyers-Ulam-Rassias stability, cubic function, additive function, quasi-Banach space, $p-$Banach spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 1