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

[21]

Park CG, 2007, INT J APPL MATH STAT, V7, P112

[22]

Rassias JM., 1992, Chinese Journal of Mathematics, V20, P185

[23] STABILITY OF LINEAR MAPPING IN BANACH-SPACES [J].

RASSIAS, TM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 72 (02) :297-280

[24]

RASSIAS TM, 1984, B SCI MATH, V108, P95

[25]

Ravi K, 2007, INT J APPL MATH STAT, V7, P143

[26]

Ravi K., 2008, International Journal of Mathematics and Statistics, V3, P36

[27]

Skof F., 1983, Rendiconti Seminario Matematico Fisico Milano, V53, P113, DOI DOI 10.1007/BF02924890

[28]

Ulam S. M., 1960, Problems in Modern Mathematics

← 1 2 3 →