About: Aleksandrov–Rassias problem

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The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved the Mazur–Ulam theorem stating that every isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation. In 1970, Aleksandr Danilovich Aleksandrov asked whether the existence of a single conservative distance for a mapping implies that it is an isometry. Themistocles M. Rassias posed the following problem:

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rdfs:label	Aleksandrov–Rassias problem (en)
rdfs:comment	The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved the Mazur–Ulam theorem stating that every isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation. In 1970, Aleksandr Danilovich Aleksandrov asked whether the existence of a single conservative distance for a mapping implies that it is an isometry. Themistocles M. Rassias posed the following problem: (en)
dcterms:subject	Mathematical analysis Functional equations Metric geometry
Wikipage page ID	30733508 (xsd:integer)
Wikipage revision ID	1108506198 (xsd:integer)
Link from a Wikipage to another Wikipage	Themistocles M. Rassias Linear mapping Stanislaw Ulam Stanisław Mazur Mazur–Ulam theorem Banach spaces Aleksandr Danilovich Aleksandrov Isometry Mathematical analysis Functional equations Metric geometry Normed vector space
Link from a Wikipage to an external page	https://www.ams.org/mathscinet/pdf/2042566.pdf%3Fpg1=IID&s1=342623&vfpref=html&r=30 https://www.ams.org/mathscinet/pdf/2101186.pdf%3Fpg1=IID&s1=342623&vfpref=html&r=27 https://www.ams.org/mathscinet/pdf/259728.pdf%3Fpg1=IID&s1=195576&vfpref=html&r=90 http://www.sciencedirect.com/science%3F_ob=MImg&_imagekey=B6WK2-4J90XNS-2-1&_cdi=6894&_user=83473&_pii=S0022247X06000564&_origin=search&_coverDate=12%2F15%2F2006&_sk=996759997&view=c&wchp=dGLbVzz-zSkWA&md5=b367c42e74e88be0355b39b2820ef35b&ie=/sdarticle.pdf https://archive.today/20130201194010/http:/www.sciencedirect.com/science%3F_ob=ArticleURL&_udi=B6WK2-457D0SY-7Y&_user=83473&_coverDate=02/01/2001&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1633108326&_rerunOrigin=google&_acct=C000059671&_version=1&_urlVersion=0&_userid=83473&md5=e2bc17e39427599d1f0d9d0708f50570&searchtype=a https://www.springer.com/mathematics/book/978-1-4614-3497-9
sameAs	Aleksandrov–Rassias problem Aleksandrov–Rassias problem Aleksandrov–Rassias problem
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has abstract	The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved the Mazur–Ulam theorem stating that every isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation. In 1970, Aleksandr Danilovich Aleksandrov asked whether the existence of a single conservative distance for a mapping implies that it is an isometry. Themistocles M. Rassias posed the following problem: Aleksandrov–Rassias Problem. If X and Y are normed linear spaces and if T : X → Y is a continuous and/or surjective mapping such that whenever vectors x and y in X satisfy , then (the distance one preserving property or DOPP), is T then necessarily an isometry? There have been several attempts in the mathematical literature by a number of researchers for the solution to this problem. (en)
prov:wasDerivedFrom	wikipedia-en:Aleksandrov–Rassias_problem?oldid=1108506198&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Aleksandrov–Rassias_problem
is Link from a Wikipage to another Wikipage of	Aleksandrov-Rassias problem Themistocles M. Rassias Mazur–Ulam theorem Aleksandr Danilovich Aleksandrov Rassias
is Wikipage redirect of	Aleksandrov-Rassias problem
is Wikipage disambiguates of	Rassias
is known for of	Themistocles M. Rassias
is known for of	Themistocles M. Rassias
is foaf:primaryTopic of	wikipedia-en:Aleksandrov–Rassias_problem

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