## Tokyo Journal of Mathematics

### On the Hyers-Ulam Stability of Real Continuous Function Valued Differentiable Map

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 24, Number 2 (2001), 467-476.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.tjm/1255958187

Digital Object Identifier
doi:10.3836/tjm/1255958187

Mathematical Reviews number (MathSciNet)
MR1874983

Zentralblatt MATH identifier
1002.39039

#### Citation

MIURA, Takeshi; TAKAHASI, Sin-ei; CHODA, Hisashi. On the Hyers-Ulam Stability of Real Continuous Function Valued Differentiable Map. Tokyo J. Math. 24 (2001), no. 2, 467--476. doi:10.3836/tjm/1255958187. https://projecteuclid.org/euclid.tjm/1255958187