International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 22, Pages 1151-1158
doi:10.1155/S0161171204304333

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

Abstract

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 |1−f′/hf|≤ϵ.