Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions
Summary: Let \(h\) be an entire function and \(T_h\) the differential operator defined by \(T_hf = f' + hf\). We show that \(T_h\) has Hyers--Ulam stability if and only if \(h\) is a nonzero constant. We also consider a Ger-type stability problem for \(|1-f'/ hf|\leq \varepsilon\).
scientific article; zbMATH DE number 2168671