About: Quasi-derivative

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In mathematics, the quasi-derivative is one of several generalizations of the derivative of a function between two Banach spaces. The quasi-derivative is a slightly stronger version of the Gateaux derivative, though weaker than the Fréchet derivative. Let f : A → F be a continuous function from an open set A in a Banach space E to another Banach space F. Then the quasi-derivative of f at x0 ∈ A is a linear transformation u : E → F with the following property: for every continuous function g : [0,1] → A with g(0)=x0 such that g′(0) ∈ E exists,

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rdfs:label	Quasi-derivative (en) Quasi-pochodna (pl)
rdfs:comment	Quasi-pochodna – jedno z uogólnień pochodnej funkcji między przestrzeniami Banacha. Quasi-pochodną można postrzegać jako silniejszą wersję pojęcia pochodnej Gâteaux, lecz z kolei słabsze niż pochodna Frécheta (w sensie opisanym ). (pl) In mathematics, the quasi-derivative is one of several generalizations of the derivative of a function between two Banach spaces. The quasi-derivative is a slightly stronger version of the Gateaux derivative, though weaker than the Fréchet derivative. Let f : A → F be a continuous function from an open set A in a Banach space E to another Banach space F. Then the quasi-derivative of f at x0 ∈ A is a linear transformation u : E → F with the following property: for every continuous function g : [0,1] → A with g(0)=x0 such that g′(0) ∈ E exists, (en)
dcterms:subject	Banach spaces Generalizations of the derivative
Wikipage page ID	15712191 (xsd:integer)
Wikipage revision ID	1119695882 (xsd:integer)
Link from a Wikipage to another Wikipage	Derivative Banach spaces Continuous function Mathematics Function (mathematics) Gateaux derivative Generalizations of the derivative Fréchet derivative Banach space Chain rule Open set Linear transformation
sameAs	Quasi-derivative Quasi-derivative Quasi-derivative Quasi-derivative Quasi-derivative
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Analysis_in_topological_vector_spaces dbt:Functional_analysis dbt:Mathanalysis-stub
has abstract	In mathematics, the quasi-derivative is one of several generalizations of the derivative of a function between two Banach spaces. The quasi-derivative is a slightly stronger version of the Gateaux derivative, though weaker than the Fréchet derivative. Let f : A → F be a continuous function from an open set A in a Banach space E to another Banach space F. Then the quasi-derivative of f at x0 ∈ A is a linear transformation u : E → F with the following property: for every continuous function g : [0,1] → A with g(0)=x0 such that g′(0) ∈ E exists, If such a linear map u exists, then f is said to be quasi-differentiable at x0. Continuity of u need not be assumed, but it follows instead from the definition of the quasi-derivative. If f is Fréchet differentiable at x0, then by the chain rule, f is also quasi-differentiable and its quasi-derivative is equal to its Fréchet derivative at x0. The converse is true provided E is finite-dimensional. Finally, if f is quasi-differentiable, then it is Gateaux differentiable and its Gateaux derivative is equal to its quasi-derivative. (en) Quasi-pochodna – jedno z uogólnień pochodnej funkcji między przestrzeniami Banacha. Quasi-pochodną można postrzegać jako silniejszą wersję pojęcia pochodnej Gâteaux, lecz z kolei słabsze niż pochodna Frécheta (w sensie opisanym ). (pl)
prov:wasDerivedFrom	wikipedia-en:Quasi-derivative?oldid=1119695882&ns=0
page length (characters) of wiki page	1828 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Quasi-derivative
is Link from a Wikipage to another Wikipage of	Quasiderivative Generalizations of the derivative Banach space Quasi-differentiable Quasidifferentiable
is Wikipage redirect of	Quasiderivative Quasi-differentiable Quasidifferentiable
is foaf:primaryTopic of	wikipedia-en:Quasi-derivative

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