摘要
This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f^(n+i)(x0)h^(n+i)=0(i=1,2,……,p-1) and f^(n+p)(x0)h^(h+p) don't exist. Meanwhile, achicve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.
This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.
基金
Supported by the Natural Seience Foundation of Henan Educational Committee(20031100036)
关键词
渐近性
非线性泛函分析
功能
均值点
functional
F-derivative
Gα-derivative
mean value point
assymptotic property
