International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 22, Pages 1151-1158

Ger-type and Hyers-Ulam stabilities for the first-order linear differential operators of entire functions

Takeshi Miura,1 Go Hirasawa,2 and Sin-Ei Takahasi1

1Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992-8510, Japan
2Department of Mathematics, Nippon Institute of Technology, Miyashiro, Saitama 345-8501, Japan

Received 22 April 2003

Copyright © 2004 Takeshi Miura 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.


Let h be an entire function and Th a differential operator defined by Thf=f+hf. We show that Th has the Hyers-Ulam stability if and only if h is a nonzero constant. We also consider Ger-type stability problem for |1f/hf|ϵ.