ON THE STABILITY OF DRYGAS FUNCTIONAL EQUATION ON GROUPS

被引：9

作者：

Faiziev, Valerii A. ^{[2
]}

Sahoo, Prasanna K. ^{[1
]}

机构：

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Tver State Agr Acad, Tver Sakharovo, Russia

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2007年 / 1卷 / 01期

关键词：

Additive character of a group; bihomomorphism; Drygas functional equation; homomorphism; Jensen functional equation; metabelian group; n-Abelian group; quadratic functional equation;

D O I：

10.15352/bjma/1240321554

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the stability of the system of functional equations f(xy) + f(xy(-1)) = 2f(x) + f(y) + f(y(-1)) and f(yx) + f(y(-1)x) = 2f(x) + f(y) + f(y(-1)) on groups. Here f is a real-valued function that takes values on a group. Among others we proved the following results: 1) the system, in general, is not stable on an arbitrary group; 2) the system is stable on Heisenberg group UT(3, K), where K is a commutative field with characteristic different from two; 3) the system is stable on certain class of n-Abelian groups; 4) any group can be embedded into a group where this system is stable.

引用

页码：43 / 55

页数：13

共 18 条

[1] FACTORIZATION OF NORMAL-SOLUBLE AND NORMAL-NILPOTENT GROUPS [J].