GENERALIZED QUADRATIC MAPPINGS IN 2d VARIABLES

被引：0

作者：

Cho, Yeol Je ^{[1
,2
]}

Lee, Sang Han ^{[3
]}

Park, Choonkil ^{[4
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[2] Gyeongsang Natl Univ, RINS, Chinju 660701, South Korea

[3] Chungbuk Prov Univ Sci & Technol, Dept Cultural Studies, Okcheon 373807, South Korea

[4] Hanyang Univ, Res Inst Nat Sci, Dept Math, Seoul 133791, South Korea

来源：

KOREAN JOURNAL OF MATHEMATICS | 2011年 / 19卷 / 01期

关键词：

Hyers-Ulam stability; quadratic mapping; functional equation;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X, Y be vector spaces. It is shown that if an even mapping f : X -> Y satisfies f(0) = 0, and 2(C-2d-2(d-1) -(2d-2) C-d)f (Sigma C-2d(j=1)d)f (Sigma(2d)(j=1) x(j)) + Sigma(tau(j)=0,1,Sigma j=12d tau(j) = d) f(Sigma(2d)(j=1) (-1)(tau(j))x(j)) = 2(C-2d-1(d) + C-2d-2(d-1) -C-2d-2(d)) Sigma(2d)(j=1) f(x(j)) for all x(1) , ... , x(2d) is an element of X, then the even mapping f : X -> Y is quadratic. Furthermore, we prove the Hyers-Ulam stability of the above functional equation in Banach spaces.

引用

页码：17 / 24

页数：8

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