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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.

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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