Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy

  • Takahasi, Sin-Ei (Department of Basic Technology, Applied Mathematics and Physics, Yamagata University) ;
  • Miura, Takeshi (Department of Basic Technology, Applied Mathematics and Physics, Yamagata University) ;
  • Miyajima, Shizuo (Department of Mathematics, Faculty of Science, Science University of Tokyo)
  • Published : 2002.05.01
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Abstract

Let I be an open interval and X a complex Banach space. Let$\varepsilon\geq0\;and\;\lambda$ a non-zero complex number with Re $\lambda\neq0$. If $\varphi$ is a strongly differentiable map from I to X with $\parallel\varphi^'(t)-\lambda\varphi(t)\parallel\leq\varepsilon\;for\;all\;t\in\;I$, then we show that the distance between $\varphi$ and the set of all solutions to the differential equation y'=$\lambda$y is at most $\varepsilon/$\mid$Re\lambda$\mid$$.

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References

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