Difference between revisions of "Strong derivative/Infobox"
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(Created page with "{{Infobox |title=Strong derivative |above=<span style="font-size:1.25em;">{{MM|1=\lim_{h\rightarrow 0}\left(\frac{T(x_0+h)-T(x_0)}{\Vert h\Vert_X}\right)=\overbrace{L_{x_0}:X\...") |
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{{Infobox | {{Infobox | ||
|title=Strong derivative | |title=Strong derivative | ||
| − | |above=<span style="font-size:1.25em;">{{MM|1=\lim_{h\rightarrow 0}\left(\frac{ | + | |above=<span style="font-size:1.25em;">{{MM|1=\lim_{h\rightarrow 0}\left(\frac{\big\Vert f(x_0+h)-f(x_0)-df\vert_{x_0}\big\Vert_Y}{\Vert h\Vert_X}\right)}}</span><br/>For two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}}<br/>and a [[mapping]] {{M|f:U\rightarrow Y}} for {{M|U}} [[open set|open]] in {{M|X}}<br/><br/>{{M|df\vert_{x_0}:X\rightarrow Y}} a [[linear map]] called the<br/>"''derivative of {{M|f}} at {{M|x_0}}''" |
}}<noinclude> | }}<noinclude> | ||
{{Stub page|This is just a stub, CHECK THE INFOBOX DEFINITION IS VALID}} | {{Stub page|This is just a stub, CHECK THE INFOBOX DEFINITION IS VALID}} | ||
[[Category:Infoboxes]] | [[Category:Infoboxes]] | ||
</noinclude> | </noinclude> | ||
Latest revision as of 14:06, 13 November 2016
| Strong derivative | |
| [math]\lim_{h\rightarrow 0}\left(\frac{\big\Vert f(x_0+h)-f(x_0)-df\vert_{x_0}\big\Vert_Y}{\Vert h\Vert_X}\right)[/math] For two normed spaces [ilmath](X,\Vert\cdot\Vert_X)[/ilmath] and [ilmath](Y,\Vert\cdot\Vert_Y)[/ilmath] and a mapping [ilmath]f:U\rightarrow Y[/ilmath] for [ilmath]U[/ilmath] open in [ilmath]X[/ilmath] [ilmath]df\vert_{x_0}:X\rightarrow Y[/ilmath] a linear map called the "derivative of [ilmath]f[/ilmath] at [ilmath]x_0[/ilmath]" |
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