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dc.contributor.authorShidama, Yasunari-
dc.date.accessioned2015-12-06T19:05:19Z-
dc.date.available2015-12-06T19:05:19Z-
dc.date.issued2012-
dc.identifier.citationFormalized Mathematics, Volume 20, Issue 1, 2012, Pages 31-40-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3625-
dc.description.abstractIn this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vector-valued functions is obtained as follows: If ||ƒ'(x + t · h)|| is bounded for t between 0 and 1 by some constant M, then ||ƒ(x + t · h) - ƒ(x)|| ≤ M · ||h||. This theorem is called the mean value theorem for vector-valued functions. By this theorem, the relation between the (total) derivative and the partial derivatives of a function is derived [23].-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.titleDifferentiable Functions on Normed Linear Spaces-
dc.typeArticle-
dc.identifier.doi10.2478/v10037-012-0005-1-
dc.description.AffiliationShinshu University, Nagano, Japan-
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Występuje w kolekcji(ach):Formalized Mathematics, 2012, Volume 20, Issue 1

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