关于泛函微分中值点渐近性的进一步讨论

Further Disussion on Asymptotic Property of the Functional Differential "Mean Value Point

本文在赋范线性空间上讨论微分中值点的渐近性 ,利用泛函的微积分理论给出了f( i) (x0 ) h( i) =0 ,g( j) (x0 ) h( j) =0 (i=1,2… n - 1,j=1.2… m - 1) ,f( n) (x0 ) h( n) ,g( m) (x0 ) h( m) 都不存在时泛函微分中值点渐近性的估计式 .

In this paper,we studied the asymptotic property of the functional differential 'mean value point' in normed linear spaces.Making use of theories of the functional differential and integral,gain the asymptotic estimation formula of the functional 'mean value point' when f (i)(x 0)h (i)=0,g (i)(x 0)h (i)=0(i=1,2...n-1,j=1,2...m-1)and f (n)(x 0)h (n),g (m)x 0h (m) do not exist.