Hyperstability of the Cauchy equation on restricted domains

被引：0
作者：
Janusz Brzdȩk
机构：
[1] Pedagogical University,Department of Mathematics
来源：
Acta Mathematica Hungarica | 2013年 / 141卷
关键词：
Cauchy equation; hyperstability; cocycle; Hyers–Ulam stability; 39B82; 47H14; 47J20; 39B62; 47H10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show that a very classical result, proved by T. Aoki, Z. Gajda and Th. M. Rassias and concerning the Hyers–Ulam stability of the Cauchy equation f(x+y)=f(x)+f(y), can be significantly improved. We also provide some immediate applications of it (among others for the cocycle equation, which is useful in characterizations of information measures). In particular, we give a solution to a problem that was formulated more than 20 years ago and concerned optimality of some estimations.
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页码：58 / 67
页数：9
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