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- Gâteaux_derivative abstract "In mathematics, the Gâteaux differential or Gâteaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René Gâteaux, a French mathematician who died young in World War I, it is defined for functions between locally convex topological vector spaces such as Banach spaces. Like the Fréchet derivative on a Banach space, the Gâteaux differential is often used to formalize the functional derivative commonly used in the calculus of variations and physics.Unlike other forms of derivatives, the Gâteaux differential of a function may be nonlinear. However, often the definition of the Gâteaux differential also requires that it be a continuous linear transformation. Some authors, such as Tikhomirov (2001), draw a further distinction between the Gâteaux differential (which may be nonlinear) and the Gâteaux derivative (which they take to be linear). In most applications, continuous linearity follows from some more primitive condition which is natural to the particular setting, such as imposing complex differentiability in the context of infinite dimensional holomorphy or continuous differentiability in nonlinear analysis.".
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- Gâteaux_derivative wikiPageWikiLinkText "Gâteaux derivative".
- Gâteaux_derivative wikiPageWikiLinkText "Gâteaux differentiability".
- Gâteaux_derivative wikiPageWikiLinkText "Gâteaux differentiable".
- Gâteaux_derivative wikiPageWikiLinkText "Gâteaux differentials".
- Gâteaux_derivative wikiPageWikiLinkText "differential".
- Gâteaux_derivative wikiPageWikiLinkText "directional derivative".
- Gâteaux_derivative first "V.M.".
- Gâteaux_derivative hasPhotoCollection Gâteaux_derivative.
- Gâteaux_derivative id "G/g043390".
- Gâteaux_derivative last "Tikhomirov".
- Gâteaux_derivative title "Gâteaux variation".
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- Gâteaux_derivative year "2001".
- Gâteaux_derivative subject Category:Generalizations_of_the_derivative.
- Gâteaux_derivative subject Category:Topological_vector_spaces.
- Gâteaux_derivative comment "In mathematics, the Gâteaux differential or Gâteaux derivative is a generalization of the concept of directional derivative in differential calculus. Named after René Gâteaux, a French mathematician who died young in World War I, it is defined for functions between locally convex topological vector spaces such as Banach spaces.".
- Gâteaux_derivative label "Gâteaux derivative".
- Gâteaux_derivative sameAs Derivada_de_Gâteaux.
- Gâteaux_derivative sameAs Gâteaux-Differential.
- Gâteaux_derivative sameAs ガトー微分.
- Gâteaux_derivative sameAs Gâteaux-afgeleide.