International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 109754, 7 pages
http://dx.doi.org/10.1155/2013/109754
Research Article

The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples

Hiroyoshi Oda,1 Makoto Tsukada,1 Takeshi Miura,2 Yuji Kobayashi,3 and Sin-Ei Takahasi4

1Department of Information Sciences, Toho University, Funabashi, Chiba 274-8501, Japan
2Yamagata University, Yonezawa, Yamagata 273-0866, Japan
3Toho University, Funabashi, Chiba 274-8501, Japan
4Toho University, Yamagata University, Funabashi, Chiba 273-0866, Japan

Received 27 December 2012; Accepted 21 February 2013

Academic Editor: Irena Lasiecka

Copyright © 2013 Hiroyoshi Oda et al. 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 give an Ulam type stability result for the following functional equation: under a suitable condition. We also give a concrete stability result for the case taking up as a control function.