Remarks on hyperstability of the Cauchy functional equation

被引：57

作者：

Brzdek, Janusz ^{[1
]}

机构：

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

来源：

AEQUATIONES MATHEMATICAE | 2013年 / 86卷 / 03期

关键词：

Cauchy equation; hyperstability; cocycle; Hyers-Ulam stability; ADDITIVE MAPPINGS; STABILITY; SPACES;

D O I：

10.1007/s00010-012-0168-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present some simple observations on hyperstability for the Cauchy equation on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense), must be actually solutions to it. In this way we demonstrate in particular that hyperstability is not a very exceptional phenomenon as it has been considered so far. We also provide some simple examples of applications of those results.

引用

页码：255 / 267

页数：13

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