Differentiable Functions on Normed Linear Spaces

Pole DC	Wartość	Język
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-06T19:05:19Z	-
dc.date.available	2015-12-06T19:05:19Z	-
dc.date.issued	2012	-
dc.identifier.citation	Formalized Mathematics, Volume 20, Issue 1, 2012, Pages 31-40	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3625	-
dc.description.abstract	In 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.iso	en	-
dc.publisher	De Gruyter Open	-
dc.title	Differentiable Functions on Normed Linear Spaces	-
dc.type	Article	-
dc.identifier.doi	10.2478/v10037-012-0005-1	-
dc.description.Affiliation	Shinshu University, Nagano, Japan	-
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