On the A. D. Aleksandrov problem of conservative distances and the Mazur-Ulam theorem

Rassias, TM

dc.contributor.author	Rassias, TM	en
dc.date.accessioned	2014-03-01T01:16:50Z
dc.date.available	2014-03-01T01:16:50Z
dc.date.issued	2001	en
dc.identifier.issn	0362-546X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14249
dc.subject	Aleksandrov problem	en
dc.subject	Mazur-Ulam theorem	en
dc.subject	isometry	en
dc.subject	Euclidean metric	en
dc.subject	sphere	en
dc.subject	Banach space	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	Differential equations	en
dc.subject.other	Set theory	en
dc.subject.other	Theorem proving	en
dc.subject.other	Aleksandrov problem	en
dc.subject.other	Mazur-Ulam theory	en
dc.subject.other	Computational geometry	en
dc.title	On the A. D. Aleksandrov problem of conservative distances and the Mazur-Ulam theorem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0362-546X(01)00381-9	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0362-546X(01)00381-9	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	Some relations between linearity and isometry are investigated in the problem of A. D. Aleksandrov and the Mazur-Ulam theorem for mappings which preserve some distance. Aleksandrov posed the problem that under what conditions is a mapping of a metric space into itself preserving unit distance an isometry. Mazur-Ulam theory proven that every isometry of a normed real vector space onto a normed real vector space is a linear mapping up to translation.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Nonlinear Analysis, Theory, Methods and Applications	en
dc.identifier.doi	10.1016/S0362-546X(01)00381-9	en
dc.identifier.isi	ISI:000170889300039	en
dc.identifier.volume	47	en
dc.identifier.issue	4	en
dc.identifier.spage	2597	en
dc.identifier.epage	2608	en