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- 2015
二元三次函数方程的解及在模糊Banach 空间上的稳定性
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Abstract:
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.
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
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