On stability of the general linear equation

被引：39

作者：

Bahyrycz, Anna ^{[1
]}

Olko, Jolanta ^{[1
]}

机构：

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

来源：

AEQUATIONES MATHEMATICAE | 2015年 / 89卷 / 06期

关键词：

Hyers-Ulam stability; linear functional equation; fixed point theorem; FUNCTIONAL-EQUATIONS;

D O I：

10.1007/s00010-014-0317-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove, using the fixed point approach, some stability results for the general linear functional equation. Namely we obtain sufficient conditions for the stability of a wide class of functional equations and control functions. Our results generalize a lot of the well known and recent outcomes concerning stability. In some examples we indicate how our method may be used to check if the particular functional equation is stable and we discuss the optimality of obtained bounding constants.

引用

页码：1461 / 1474

页数：14

共 17 条

[1]

[Anonymous], 1983, Rend. Semin. Mat. Fis. Milano, DOI DOI 10.1007/BF02924890

[2]

[Anonymous], J MATH ANAL APPL

[3]

[Anonymous], 1994, Stability of Mappings of Hyers-Ulam Type

[4]

[Anonymous], REAL ANAL EXCHANGE