On approximate solutions of the linear functional equation of higher order

被引：23

作者：

Brzdek, Janusz ^{[2
]}

Popa, Dorian ^{[3
]}

Xu, Bing ^{[1
]}

机构：

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

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

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 373卷 / 02期

关键词：

Approximate solution; Banach space; Characteristic root; Linear functional equation; Hyers-Ulam stability; HYERS-ULAM STABILITY;

D O I：

10.1016/j.jmaa.2010.08.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that, under some assumptions, every approximate solution of the linear functional equation of higher order, in single variable, generates a solution of the equation that is close to it. We also give a description of a procedure that yields such a solution, estimate the distance between those approximate and exact solutions to the equation, and discuss the problem of uniqueness. Moreover, as a consequence we obtain some results concerning the Hyers-Ulam stability of the equation. (c) 2010 Elsevier Inc. All rights reserved.

引用

页码：680 / 689

页数：10

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