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

- Journal title : Journal of the Korean Mathematical Society
- Volume 41, Issue 6, 2004, pp.995-1005
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2004.41.6.995

Title & Authors

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

Miura, Takeshi Miura; Jung, Soon-Mo; Takahasi, Sin-Ei;

Miura, Takeshi Miura; Jung, Soon-Mo; Takahasi, Sin-Ei;

Abstract

The aim of this paper is to prove the stability in the sense of Hyers-Ulam- Rassias of the Banach space valued differentialequation y' = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y' = λy, then there exists an exact solution of the equation near to f.

Keywords

Hyers-Ulam-Rassias stability;differential equation;

Language

English

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