Original Article
Kyungpook Mathematical Journal 2010; 50(4): 557-564
Published online December 23, 2010
Copyright © Kyungpook Mathematical Journal.
A Fixed Point Approach to the Stability of a Functional Equa-
tion
Won-Gil Park, Jae-Hyeong Bae
Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Korea,
Jae-Hyeong Bae, College of Liberal Arts, Kyung Hee University, Yongin 446-701, Korea
Received: December 23, 2010; Revised: December 23, 2010; Accepted: December 23, 2010
y using an idea of Cu{a}dariu and Radu cite{CR03}, we prove the
generalized Hyers-Ulam stability of the functional equation
$$f(x+y,z-w)+f(x-y,z+w)=2f(x,z)+2f(y,w).$$
The quadratic form $f:R R oR$ given by $f(x,y)=ax^2+by^2$ is a solution
of the above functional equation.
Keywords: Alternative of xed point, Functional equation, Stability