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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Strict differentiability ： ウィキペディア英語版 Strict differentiability In mathematics, strict differentiability is a modification of the usual notion of differentiability of functions that is particularly suited to p-adic analysis. In short, the definition is made more restrictive by allowing both points used in the difference quotient to "move". == Basic definition == The simplest setting in which strict differentiability can be considered, is that of a real-valued function defined on an interval ''I'' of the real line. The function ''f'':''I''→R is said ''strictly differentiable'' in a point ''a''∈''I'' if :$\backslash lim\_\backslash frac$ exists, where $(x,y)\backslash to(a,a)$ is to be considered as limit in $\backslash mathbf^2$, and of course requiring $x\backslash ne\; y$. A strictly differentiable function is obviously differentiable, but the converse is wrong, as can be seen from the counter-example $f(x)=x^2\backslash sin\backslash tfrac,\backslash \; f(0)=0,~x\_n=\backslash tfrac,\backslash \; y\_n=x\_$. One has however the equivalence of strict differentiability on an interval ''I'', and being of differentiability class $C^1(I)$. The previous definition can be generalized to the case where R is replaced by a normed vector space ''E'', and requiring existence of a continuous linear map ''L'' such that :$f(x)-f(y)=L(x-y)+o((x,y)-(a,a))$ where $o(\backslash cdot)$ is defined in a natural way on ''E×E''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Strict differentiability」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.