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- Quasi-derivative 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 Gâteaux 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 Gâteaux differentiable and its Gâteaux derivative is equal to its quasi-derivative.".
- Quasi-derivative wikiPageID "15712191".
- Quasi-derivative wikiPageRevisionID "599073709".
- Quasi-derivative hasPhotoCollection Quasi-derivative.
- Quasi-derivative subject Category:Banach_spaces.
- Quasi-derivative subject Category:Generalizations_of_the_derivative.
- Quasi-derivative type Abstraction100002137.
- Quasi-derivative type Association105763916.
- Quasi-derivative type Attribute100024264.
- Quasi-derivative type BanachSpaces.
- Quasi-derivative type BasicCognitiveProcess105701944.
- Quasi-derivative type Cognition100023271.
- Quasi-derivative type Colligation105764197.
- Quasi-derivative type Generalization105774415.
- Quasi-derivative type GeneralizationsOfTheDerivative.
- Quasi-derivative type Memory105760202.
- Quasi-derivative type Process105701363.
- Quasi-derivative type PsychologicalFeature100023100.
- Quasi-derivative type Space100028651.
- Quasi-derivative comment "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 Gâteaux 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.".
- Quasi-derivative label "Quasi-derivative".
- Quasi-derivative label "Quasi-pochodna".
- Quasi-derivative sameAs Quasi-pochodna.
- Quasi-derivative sameAs m.03nqzv6.
- Quasi-derivative sameAs Q7269446.
- Quasi-derivative sameAs Q7269446.
- Quasi-derivative sameAs Quasi-derivative.
- Quasi-derivative wasDerivedFrom Quasi-derivative?oldid=599073709.
- Quasi-derivative isPrimaryTopicOf Quasi-derivative.