Journal of Applied Mathematics
Volume 2011 (2011), Article ID 817079, 16 pages
http://dx.doi.org/10.1155/2011/817079
Research Article

A Fixed Point Approach to the Stability of the Cauchy Additive and Quadratic Type Functional Equation

Sun Sook Jin and Yang-Hi Lee

Department of Mathematics Education, Gongju National University of Education, Gongju 314-711, Republic of Korea

Received 2 June 2011; Accepted 18 July 2011

Academic Editor: Yuri Sotskov

Copyright © 2011 Sun Sook Jin and Yang-Hi Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the stability of the functional equation 2 𝑓 ( 𝑥 + 𝑦 ) + 𝑓 ( 𝑥 − 𝑦 ) + 𝑓 ( 𝑦 − 𝑥 ) − 3 𝑓 ( 𝑥 ) − 𝑓 ( − 𝑥 ) − 3 𝑓 ( 𝑦 ) − 𝑓 ( − 𝑦 ) = 0 by using the fixed point theory in the sense of Cădariu and Radu.