Functional Equations Related to Inner Product Spaces

被引：4

作者：

Park, Choonkil ^{[2
]}

Park, Won-Gil ^{[1
]}

Najati, Abbas ^{[3
]}

机构：

[1] Natl Inst Math Sci, Taejon 305340, South Korea

[2] Hanyang Univ, Dept Math, Seoul 133791, South Korea

[3] Univ Mohaghegh Ardabili, Fac Sci, Dept Math, Ardebil 51664, Iran

来源：

ABSTRACT AND APPLIED ANALYSIS | 2009年

基金：

新加坡国家研究基金会;

关键词：

ADDITIVE MAPPINGS; NORMED SPACES; STABILITY;

D O I：

10.1155/2009/907121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let V,W be real vector spaces. It is shown that an odd mapping f : V -> W satisfies Sigma(2n)(i-1)f(x(i) - 1/wn Sigma(2n)(j=1)x(j)) = Sigma(2n)(i=1)f(x(i)) - 2nf(1/2n Sigma(2n)(i=1)x(i)) for all x(1), ..., x(2n) is an element of V if and only if the odd mapping f : V -> W is Cauchy additive. Furthermore, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces. Copyright (C) 2009 Choonkil Park et al.

引用

页数：11

共 28 条

[1]

[Anonymous], 2006, DEMONSTR MATH

[2]

[Anonymous], NONLINEAR FUNCT ANAL

[3]

[Anonymous], 1995, ANN MATH BLAISE PASC

[4]

[Anonymous], 1999, ADV EQU INEQUAL HADR

[5]

[Anonymous], 2007, INT J MATH MATH SCI, DOI DOI 10.1155/2007/63239

[6]

Aoki T., 1950, J. Math. Soc. Japan, V2, P64

[7]

Bouikhalene B., 2007, Int. J. Appl. Math. Stat., V7, P27

[8]

Cholewa P.W., 1984, Aequat. Math, V27, P76, DOI [10.1007/BF02192660, DOI 10.1007/BF02192660]

[9] ON THE STABILITY OF THE QUADRATIC MAPPING IN NORMED SPACES [J].

CZERWIK, S .

ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 1992, 62 :59-64

[10] A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF APPROXIMATELY ADDITIVE MAPPINGS [J].

GAVRUTA, P .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1994, 184 (03) :431-436

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