IJPAM: Volume 48, No. 2 (2008)

STABILITY OF FUNCTIONAL EQUATION
IN QUASI-BANACH SPACES

K. Ravi$^1$, R. Kodandan$^2$, N. Jammuna$^3$
$^1$Department of Mathematics
Sacred Heart College
Tamil Nadu, Tirupattur, 635 601, INDIA
e-mail: shckravi@yahoo.co.in
$^2$Department of Mathematics
Srinivasa Institute of Technology and Management Studies
Chittoor, Andhra Pradesh, 517 127, INDIA
e-mail: rkodandan1979@rediff.co.in
$^3$Department of Mathematics
Magna College of Engineering
Red Hills, Tiruvallur High Road, Chennai, 600 055, INDIA


Abstract.In this paper, we introduce and investigate the general solution of a new functional equation

\begin{displaymath}f(3x+y)+f(3x-y) = f(x+y)+f(x-y)+f(4x)\end{displaymath}

and discuss its Hyers-Ulam-Rassias stability in quasi-Banach spaces.

Received: August 19, 2008

AMS Subject Classification: 39B52, 39B82, 39B72, 46B03, 47Jxx

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 2