Hyers-Ulam stability of an n-apollonius type quadratic mapping

被引：29

作者：

Najati, Abbas ^{[1
]}

机构：

[1] Univ Mohaghegh Ardabili, Fac Sci, Dept Math, Ardebil, Iran

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2007年 / 14卷 / 04期

关键词：

Apollonius' identity; n - Apollonius' identity; Hyers - Ulam stability; quadratic function; quadratic functional equation of Apollonius type; quadratic functional equation of n - Apollonius type;

D O I：

10.36045/bbms/1195157142

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X and Y be linear spaces. It is shown that for a fixed positive integer n >= 2, if a mapping Q : X -> Y satisfies the following functional equation [GRAPHICS] for all Z, x(1), ..., x(n) is an element of X, then the mapping Q : X -> Y is a quadratic mapping of Apollonius type and a quadratic mapping. We moreover prove the Hyers - Ulam stability of the functional equation (1) in Banach spaces.

引用

页码：755 / 774

页数：20

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