Matches in DBpedia 2016-04 for { <http://wikidata.dbpedia.org/resource/Q5054347> ?p ?o }
Showing triples 1 to 29 of
29
with 100 triples per page.
- Q5054347 subject Q7211696.
- Q5054347 subject Q7216206.
- Q5054347 subject Q8475379.
- Q5054347 abstract "A classical problem of Stanislaw Ulam in the theory of functional equations is the following: When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E? In 1941, Donald H. Hyers gave a partial affirmative answer to this question in the context of Banach spaces. This was the first significant breakthrough and a step towards more studies in this domain of research. Since then, a large number of papers have been published in connection with various generalizations of Ulam's problem and Hyers' theorem. In 1978, Themistocles M. Rassias succeeded in extending the Hyers' theorem by considering an unbounded Cauchy difference. He was the first to prove the stability of the linear mapping in Banach spaces. In 1950, T. Aoki had provided a proof of a special case of the Rassias' result when the given function is additive. For an extensive presentation of the stability of functional equations in the context of Ulam's problem, the interested reader is referred to the recent book of S.-M. Jung, published by Springer, New York, 2011 (see references below).Th. M. Rassias' theorem attracted a number of mathematicians who began to be stimulated to do research in stability theory of functional equations. By regarding the large influence of S. M. Ulam, D. H. Hyers and Th. M. Rassias on the study of stability problems of functional equations, this concept is called the Hyers–Ulam–Rassias stability.In the special case when Ulam's problem accepts a solution for the Cauchy functional equation f(x + y) = f(x) + f(y), the equation E is said to satisfy the Cauchy–Rassias stability. The name is referred to Augustin-Louis Cauchy and Themistocles M. Rassias.".
- Q5054347 wikiPageExternalLink jmi-03-26.pdf.
- Q5054347 wikiPageExternalLink 1261735234.
- Q5054347 wikiPageExternalLink 1262271387.
- Q5054347 wikiPageExternalLink S0002-9939-1978-0507327-1.pdf.
- Q5054347 wikiPageExternalLink 2242776.pdf?pg1=INDI&s1=620744&vfpref=html&r=80.
- Q5054347 wikiPageExternalLink parpl.pdf.
- Q5054347 wikiPageExternalLink view.jsp?issn=1015-8634&vol=47&no=5&sp=987.
- Q5054347 wikiPageExternalLink pnas01627-0030.pdf.
- Q5054347 wikiPageExternalLink S0022247X07008414.
- Q5054347 wikiPageExternalLink science?_ob=ArticleURL&_udi=B6WK2-4CKFHWX-B&_user=83473&_coverDate=08%2F01%2F2004&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000059671&_version=1&_urlVersion=0&_userid=83473&md5=7f53b2a640ab31090a394f3aaeac9ffe&searchtype=a.
- Q5054347 wikiPageExternalLink sdarticle.pdf.
- Q5054347 wikiPageExternalLink 978-1-4614-3497-9.
- Q5054347 wikiPageExternalLink j7660635qh228m81.
- Q5054347 wikiPageExternalLink x028947u824586lu.
- Q5054347 wikiPageWikiLink Q234357.
- Q5054347 wikiPageWikiLink Q594452.
- Q5054347 wikiPageWikiLink Q5955764.
- Q5054347 wikiPageWikiLink Q5984090.
- Q5054347 wikiPageWikiLink Q680611.
- Q5054347 wikiPageWikiLink Q7211696.
- Q5054347 wikiPageWikiLink Q7216206.
- Q5054347 wikiPageWikiLink Q8475379.
- Q5054347 wikiPageWikiLink Q8814.
- Q5054347 comment "A classical problem of Stanislaw Ulam in the theory of functional equations is the following: When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E? In 1941, Donald H. Hyers gave a partial affirmative answer to this question in the context of Banach spaces. This was the first significant breakthrough and a step towards more studies in this domain of research.".
- Q5054347 label "Cauchy–Rassias stability".