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

共 50 条

[1] Hyers-Ulam stability of a generalized Apollonius type quadratic mapping
Park, Chun-Gil
Rassias, Themistocles M.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 322 (01) : 371 - 381
[2] HYERS-ULAM STABILITY OF THE QUADRATIC FUNCTIONAL EQUATION
Elqorachi, E.
Manar, Y.
Rassias, Th. M.
INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2010, 1 (02): : 26 - 35
[3] Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping
Kenary, Hassan Azadi
Rassias, Themistocles M.
Rezaei, H.
Talebzadeh, S.
Park, Won-Gil
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2012, 2012
[4] Fixed points of a mapping and Hyers-Ulam stability
Badora, Roman
Brzdek, Janusz
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 413 (01) : 450 - 457
[5] Generalized Hyers-Ulam Stability of Quadratic Functional Inequality
Kim, Hark-Mahn
Jun, Kil-Woung
Son, Eunyoung
ABSTRACT AND APPLIED ANALYSIS, 2013,
[6] On the Asymptoticity Aspect of Hyers-Ulam Stability of Quadratic Mappings
A Rahimi
A Najati
J-H Bae
Journal of Inequalities and Applications, 2010
[7] On the Asymptoticity Aspect of Hyers-Ulam Stability of Quadratic Mappings
Rahimi, A.
Najati, A.
Bae, J. -H.
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,
[8] On the Generalized Hyers-Ulam Stability of an n-Dimensional Quadratic and Additive Type Functional Equation
Lee, Yang-Hi
JOURNAL OF APPLIED MATHEMATICS, 2014,
[9] Hyers-Ulam stability of an Euler-Lagrange type additive mapping
Park, Chun-Gil
Rassias, John Michael
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2007, 7 (F07): : 112 - 125
[10] On the Hyers-Ulam stability of the functional equations that have the quadratic property
Jung, SM
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 222 (01) : 126 - 137

← 1 2 3 4 5 →