IJPAM: Volume 86, No. 6 (2013)

ADDITIVE QUADRATIC FUNCTIONAL EQUATION ARE
STABLE IN BANACH SPACE: A FIXED POINT APPROACH

M. Arunkumar$^1$, P. Agilan$^2$
$^1$Department of Mathematics
Government Arts College
Tiruvannamalai, 606 603, TamilNadu, INDIA
Department of Mathematics
S.K.P. Engineering College
Tiruvannamalai, 606 611, TamilNadu, INDIA


Abstract. In this paper, the authors established the generalized Ulam - Hyers stability of a mixed type Additive Quadratic(AQ)-functional equation
\begin{multline*} f(x+2y+3z)+f(x-2y+3z)+f(x+2y-3z)+f(x-2y-3z)\\ = 4f(x)+8[f(y)+f(-y)]+18[f(z)+f(-z)] \end{multline*}
in Banach spaces using fixed point approach.

Received: May 9, 2013

AMS Subject Classification: 39B52, 32B72, 32B82

Key Words and Phrases: additive functional equations, quadratic functional equation, mixed type functional equation, Ulam-Hyers stability, fixed point

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DOI: 10.12732/ijpam.v86i6.8 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 6