ON FUNCTIONAL INEQUALITIES ASSOCIATED WITH JORDAN-VON NEUMANN TYPE FUNCTIONAL EQUATIONS

被引：0
作者：
An, Jong Su [1 ]
机构：
[1] Pusan Natl Univ, Dept Math Educ, Pusan 609735, South Korea
来源：
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2008年 / 23卷 / 03期
关键词：
Jordan-von Neumann type bi-additive functional equation; Jordan-von Neumann type additive-quadratic functional equation; Hyers-Ulam-Rassias stability; functional inequality;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, it is shown that if f satisfies the following functional inequality (0.1) parallel to Sigma(3)(i,j=1) f(x(i), y(j))parallel to <= parallel to f(x(1) + x(2) + x(3), y(1) + y(2) + y(3)) parallel to then f is a bi-additive mapping. We moreover prove that if f satisfies the following functional inequality (0.2). parallel to 2 Sigma(3)(j= 1) f(x(j), z) + 2 Sigma(3)(j= 1) f(x(j), w) - f( Sigma(3)(j= 1) x(j), z - w)parallel to <= parallel to f( Sigma(3)(j= 1) x(j), z + w)parallel to then f is an additive-quadratic mapping.
引用
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页码：371 / 376
页数：6
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