title: On the strong continuity of convex functions
metadata.name: dc.contributor.author
metadata.value: Malozemov, Vassili N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Plotkin, Artem V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tamasyan, Grigoriy Sh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:36:42Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:36:42Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malozemov V.N., Plotkin A.V., Tamasyan G. Sh. On the strong continuity of convex functions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 411–416.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.305
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14884
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A convex function defined on an open convex set is known to be continuous at every
  point of this set. In actuality, a convex function has a strengthened continuity property.
  In this paper, we introduce the notion of strong continuity and demonstrate that a convex
  function possesses this property. The proof is based only on the definition of convexity and
  the Jensen’s inequality. A distinct constant (constant of strong continuity) is included in
  the definition of strong continuity. In the article, we give an unimprovable value for this
  constant in the case of convex functions. The constant of strong continuity depends, in
  particular, on the form of the norm introduced in the space of the arguments of a convex
  function. Polyhedral norm is of particular interest. With its use the constant of strong
  continuity can be easily calculated. This requires a finite number of values of the convex
  function.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: convex function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong continuity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: constant of strong continuity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the strong continuity of convex functions
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 05-Malozemov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14884/1/05-Malozemov.pdf
resources.format: Adobe PDF
resources.size: 250,65 kB