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

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 39, Issue 2, 2002, pp.309-315
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2002.39.2.309

Title & Authors

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

Takahasi, Sin-Ei; Miura, Takeshi; Miyajima, Shizuo;

Takahasi, Sin-Ei; Miura, Takeshi; Miyajima, Shizuo;

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 $\varepsilon/Re\lambda$.

Keywords

exponential functions;Hyers-Ulam stability;

Language

English

Cited by

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HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′ = λy,;;;

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ESSENTIAL NORMS AND STABILITY CONSTANTS OF WEIGHTED COMPOSITION OPERATORS ON C(X),;;;

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