山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 60-66.doi: 10.6040/j.issn.1671-9352.0.2014.349
綦伟青1, 纪培胜2, 卢海宁2
QI Wei-qing1, JI Pei-sheng2, LU Hai-ning2
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.
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