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December 2001 On the Hyers-Ulam Stability of Real Continuous Function Valued Differentiable Map
Hisashi CHODA, Takeshi MIURA, Sin-ei TAKAHASI
Tokyo J. Math. 24(2): 467-476 (December 2001). DOI: 10.3836/tjm/1255958187

Abstract

We consider a differentiable map $f$ from an open interval to a real Banach space of all bounded continuous real-valued functions on a topological space. We show that $f$ can be approximated by the solution to the differential equation $x'(t)=\lambda x(t)$, if $||f'(t)-\lambda f(t)||_\infty\leq\varepsilon$ holds.

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Hisashi CHODA. Takeshi MIURA. Sin-ei TAKAHASI. "On the Hyers-Ulam Stability of Real Continuous Function Valued Differentiable Map." Tokyo J. Math. 24 (2) 467 - 476, December 2001. https://doi.org/10.3836/tjm/1255958187

Information

Published: December 2001
First available in Project Euclid: 19 October 2009

zbMATH: 1002.39039
MathSciNet: MR1874983
Digital Object Identifier: 10.3836/tjm/1255958187

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

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Vol.24 • No. 2 • December 2001
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