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On the Hyers-Ulam stability of the Banach space-valued differential equation $$y'=\lambda y$$. (English) Zbl 1011.34046
The Hyers-Ulam stability is analyzed for the differential equation $$y'=\lambda y$$, where $$y$$ maps an open interval of $$\mathbb{R}$$ into a complex Banach space. The authors prove a sufficient condition that allows one to estimate the distance between some given function $$\varphi$$ and the set of all solutions to the differential equation above.

##### MSC:
 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 34G10 Linear differential equations in abstract spaces 26D10 Inequalities involving derivatives and differential and integral operators
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