Hyers-ulam stability for linear equations of higher orders

被引：30

作者：

Brzdek, J. ^{[1
]}

Popa, D. ^{[2
]}

Xu, B. ^{[3
]}

机构：

[1] Pedag Univ, Dept Math, PL-30084 Krakow, Poland

[2] Tech Univ, Dept Math, Cluj Napoca 400020, Romania

[3] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

来源：

ACTA MATHEMATICA HUNGARICA | 2008年 / 120卷 / 1-2期

关键词：

Hyers-Ulam stability; linear functional equation; single variable; Banach space;

D O I：

10.1007/s10474-007-7069-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, in the classes of functions with values in a real or complex Banach space, the problem of Hyers-Ularn stability of a linear functional equation of higher order (with constant coefficients) can be reduced to the problem of stability of a first order linear functional equation. As a consequence we prove that (under some weak additional assumptions) the linear equation of higher order, with constant coefficients, is stable in the case where its characteristic equation has no complex roots of module one. We also derive some results concerning solutions of the equation.

引用

页码：1 / 8

页数：8

共 20 条

[1] Stability of functional equations in single variable [J].