Ger-type and Hyers-Ulam stabilities for the first-order linear differential operators of entire functions
Takeshi Miura,1Go Hirasawa,2and Sin-Ei Takahasi1
Received22 Apr 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.