IJPAM: Volume 81, No. 2 (2012)

A FIXED POINT APPROACH TO THE GENERALIZED
HYERS-ULAM STABILITY OF A MIXED
TYPE FUNCTIONAL EQUATION

Yang-Hi Lee$^1$, Soon-Mo Jung$^2$
$^1$Department of Mathematics Education
Gongju National University of Education
Gongju, 314-711, KOREA
$^2$Mathematics Section
College of Science and Technology
Hongik University
339-701, Jochiwon, KOREA


Abstract. In this paper, we investigate the stability of a functional equation
\begin{multline*}
f(x+y+z) + f(x-y+z) + f(x+y-z) + f(-x+y+z) \\
= 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z)
\end{multline*}
by using the fixed point theory in the sense of Cădariu and Radu.

Received: July 10, 2012

AMS Subject Classification: 39B82, 39B52

Key Words and Phrases: generalized Hyers-Ulam stability, fixed point method, mixed type functional equation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 2