Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y′ = λy

被引：71

作者：

Miura, T ^{[1
]}

Jung, SM

Takahasi, SE

机构：

[1] Yamagata Univ, Dept Basic Technol Appl Math & Phys, Yonezawa, Yamagata 9928510, Japan

[2] Hongik Univ, Coll Sci & Technol, Math Sect, Jochiwon 339701, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2004年 / 41卷 / 06期

关键词：

Hyers-Ulam-Rassias stability; differential equation;

D O I：

10.4134/JKMS.2004.41.6.995

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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' = lambday, 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' = lambday, then there exists an exact solution of the equation near to f.

引用

页码：995 / 1005

页数：11

共 12 条

[1] On some inequalities and stability results related to the exponential function [J].

Alsina, C ;

Ger, R .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 1998, 2 (04) :373-380

[2]

[Anonymous], 1964, PROBLEMS MODERN MATH

[3]

Gajda Z, 1991, INT J MATH MATH SCI, V14, P431, DOI [DOI 10.1155/S016117129100056X, 10.1155/S016117129100056X]

[4] On the stability of the linear functional equation [J].

Hyers, DH .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1941, 27 :222-224

[5]

JUNG SM, IN PRESS HYERS ULAM

[6] A characterization of Hyers-Ulam stability of first order linear differential operators [J].

Miura, T ;

Miyajima, S ;

Takahasi, SE .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 286 (01) :136-146

[7] Hyers-Ulam stability of linear differential operator with constant coefficients [J].

Miura, T ;

Miyajima, S ;

Takahasi, SE .

MATHEMATISCHE NACHRICHTEN, 2003, 258 :90-96

[8] ON THE BEHAVIOR OF MAPPINGS WHICH DO NOT SATISFY HYERS-ULAM STABILITY [J].

RASSIAS, TM ;

SEMRL, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 114 (04) :989-993

[9] STABILITY OF LINEAR MAPPING IN BANACH-SPACES [J].

RASSIAS, TM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 72 (02) :297-280

[10]

Rudin W., 1987, REAL COMPLEX ANAL

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