摘要
在赋范线性空间中给出了泛函的高阶微分中值定理,并利用Stirling数这个工具分别研究了当g(n)(x0)h(n)≠0且存在k(k>n),使得f(k)(x0)h(k)·gn(x0)h(n)≠f(n)(x0)h(n)·g(k)(x0)h(k)和g(n)(x0)h(n)=0,g(k)(x0)h(k)≠0(k>n),f(n)(x0)h(n)=0,f(m)(x0)h(m)≠0(m>n)时高阶微分"中值点"的渐近性,给出了渐近估计式.
The theorem of mean is given for high order differential of the functional in normed linear spaces, by using the Stirling number, and the asymptotic property is studied of 'mean value point' for high order differential of the functional respectively when g(n)(x0)h(n)≠0, exist k>n, such that f(k)(x0)h(k)·g(n)(x0)h(n)≠f(n)(x0)h(n) ·g(k)(x0)h(k)and g(n)(x0)h(n)=0,g(k)(x0)h(k)≠0(k>n),f(n)(x0)h(n)=0.f(m)(x0)h(m)≠0(m>0).The asymptotic estimation formula is obtained.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2003年第3期23-27,共5页
Journal of Shaanxi Normal University：Natural Science Edition
基金
河南省教育厅自然科学基金资助项目(20031100036)
