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Open AccessMathematics

ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy

Sin-Ei Takahasi, T. Miura, S. Miyajima

2002.5.1Bulletin of the Korean Mathematical Society

DOI: 10.4134/bkms.2002.39.2.309

Abstract

Let I be an open interval and X a complex Banach space. Let a non-zero complex number with Re . If is a strongly differentiable map from I to X with , then we show that the distance between and the set of all solutions to the differential equation y'=y is at most $\varepsilon/Re\lambda$.

Citation format

TAKAHASI, Sin-Ei; MIURA, T.; MIYAJIMA, S. ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy. Bulletin of the Korean Mathematical Society, 2002, 39: 309–315.