The stability of monomial functions on a restricted domain

被引：0

作者：

Wolna D. ^{[1
,2
]}

机构：

[1] Instytut Matematyki i Informatyki, Akademii im. Jana Długosza, PL-42-200 Czȩstochowa

[2] Instytut Matematyki, Uniwersytet Śla̧ski, PL-40-007 Katowice

来源：

aequationes mathematicae | 2006年 / 72卷 / 1-2期

关键词：

Abelian group; Functional equations; Functional inequality; Monomial function; Normed space; Stability;

D O I：

10.1007/s00010-006-2832-z

中图分类号：

学科分类号：

摘要：

Let ( G\0 ) be a power-associative and square-symmetric groupoid, Y a Banach space. We prove that a mapping f : G → Y is a monomial function of degree m if and only if for every δ > 0 there exists a weakly bounded set V δ ⊂ G such that ||Δ m yf(x) - m!f(y)||≤ δ, (xy) ∉ V δ × Vδ. © Birkhäuser Verlag, Basel, 2006.

引用

页码：100 / 109

页数：9

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