%0 Journal Article
%T 二元三次函数方程的解及在模糊Banach 空间上的稳定性<br>General solution and stability of bi-cubic functional equation
%A 綦伟青
%A 纪培胜
%A 卢海宁&lt
%A br&gt
%A QI Wei-qing
%A JI Pei-sheng
%A LU Hai-ning
%J 山东大学学报（理学版）
%D 2015
%R 10.6040/j.issn.1671-9352.0.2014.349
%X 摘要： 设X和Y是实向量空间,映射f:X2→Y称为二元三次函数,？x1,x2,y1,y2∈X,都满足下面的二元三次函数方程: f(2x1+x2,2y1+y2)+f(2x1+x2,2y1-y2)+f(2x1-x2,2y1+y2)+ f(2x1-x2,2y1-y2)=4f(x1+x2,y1+y2)+4f(x1-x2,y1+y2)+24f(x1,y1+y2)+ 4f(x1+x2,y1-y2)+4f(x1-x2,y1-y2)+24f(x1,y1-y2)+24f(x1+x2,y1)+ 24f(x1-x2,y1)+144f(x1,y1). 研究二元三次函数方程解的一般形式,证明了在模糊Banach空间上该方程的Hyers-Ulam稳定性.<br>Abstract: Let X and Y be real vector spaces. A mapping f:X2→Y is called bi-cubic if it satisfies f(2x1+x2,2y1+y2)+f(2x1+x2,2y1-y2)+f(2x1-x2,2y1+y2)+ f(2x1-x2,2y1-y2)=4f(x1+x2,y1+y2)+4f(x1-x2,y1+y2)+24f(x1,y1+y2)+ 4f(x1+x2,y1-y2)+4f(x1-x2,y1-y2)+24f(x1,y1-y2)+24f(x1+x2,y1)+ 24f(x1-x2,y1)+144f(x1,y1) for all x1,x2,y1,y2∈X. The solution of this equation is obtained and the Hyers-Ulam stability of it is proved on fuzzy Banach spaces
%K 二元三次函数方程
%K 三次函数方程
%K Hyers-Ulam稳定性
%K 模糊Banach空间
%K &lt
%K br&gt
%K Hyers-Ulam stability
%K cubic functional equation
%K bi-cubic functional equation
%K fuzzy Banach space
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2014.349