Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations ${y}' = \lambda y$

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

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2004; 41(6): 995-1005

Printed November 1, 2004

Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations ${y}' = \lambda y$

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

Yamagata University, Hong-Ik University, Yamagata University

Abstract

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Abstract

The aim of this paper is to prove the stability in the sense of Hyers-Ulam-Rassias of the Banach space valued differential equation $y' = \lambda y$, where $\lambda$ 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 $y' = \lambda y$, then there exists an exact solution of the equation near to $f$.

Keywords: Hyers-Ulam-Rassias stability, differential equation

MSC numbers: Primary 26D10; secondary 34A40