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Weak statistical convergence and weak filter convergence for unbounded sequences

Kadets, Vladimir; Leonov, Alexander; Orhan, Cihan


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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/25141</identifier>
  <creators>
    <creator>
      <creatorName>Kadets, Vladimir</creatorName>
      <givenName>Vladimir</givenName>
      <familyName>Kadets</familyName>
      <affiliation>Kharkov Natl Univ, Dept Mech &amp; Math, UA-61077 Kharkov, Ukraine</affiliation>
    </creator>
    <creator>
      <creatorName>Leonov, Alexander</creatorName>
      <givenName>Alexander</givenName>
      <familyName>Leonov</familyName>
      <affiliation>Kharkov Natl Univ, Dept Mech &amp; Math, UA-61077 Kharkov, Ukraine</affiliation>
    </creator>
    <creator>
      <creatorName>Orhan, Cihan</creatorName>
      <givenName>Cihan</givenName>
      <familyName>Orhan</familyName>
      <affiliation>Ankara Univ, Fac Sci, Dept Math, TR-06100 Ankara, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Weak Statistical Convergence And Weak Filter Convergence For Unbounded Sequences</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2010</publicationYear>
  <dates>
    <date dateType="Issued">2010-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/25141</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1016/j.jmaa.2010.05.031</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
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  <descriptions>
    <description descriptionType="Abstract">For every weakly statistically convergent sequence (x(n)) with increasing norms in a Hilbert space we prove that sup(n) parallel to x(n)parallel to/root n &amp;lt; infinity This estimate is sharp We study analogous problem for sonic other types of weak filter convergence. in particular for the Erdos-Ulam filters, analytical P-filters and F-sigma filters We present also a refinement of the recent Aron-Garcia-Maestre result on weakly dense sequences that tend to infinity in norm (C) 2010 Elsevier Inc. All rights reserved.</description>
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