<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2022000200193</article-id>
<article-id pub-id-type="doi">10.18273/revint.v40n2-2022004</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Determinant Inequalities for Positive Definite Matrices Via Additive and Multiplicative Young Inequalities]]></article-title>
<article-title xml:lang="es"><![CDATA[Desigualdades determinantes para matrices definidas positivas a través de desigualdades young aditivas y multiplicativas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[DRAGOMIR]]></surname>
<given-names><![CDATA[SILVESTRU SEVER]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Victoria University  ]]></institution>
<addr-line><![CDATA[Melbourne ]]></addr-line>
<country>Australia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>40</volume>
<numero>2</numero>
<fpage>193</fpage>
<lpage>206</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2022000200193&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2022000200193&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2022000200193&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT. In this paper we prove among others that, if the positive definite matrices A, B of order n satisfy the condition 0 &lt; mIn &#8804; B &#8722; A &#8804; M In, for some constants 0 &lt; m &lt; M, where In is the identity matrix, then 0 &#8804; (1 &#8722; t) [det (A)]&#8722;1 + t [det (A + mIn)]&#8722;1 &#8722; [det (A + mtIn)]&#8722;1 &#8804; (1 &#8722; t) [det (A)]&#8722;1 + t [det (B)]&#8722;1 &#8722; [det ((1 &#8722; t) A + tB)]&#8722;1 &#8804; (1 &#8722; t) [det (A)]&#8722;1 + t [det (A + M In)]&#8722;1 &#8722; [det (A + M tIn)]&#8722;1 , for all t &#8712; [0, 1] .  MSC2010:  47A63, 26D15, 46C05.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN. En este trabajo demostramos entre otros que, si las matrices defi-nidas positivas A, B de orden n satisfacen la condición 0&lt; mIn &#8804; B &#8722; A &#8804; M In, para algunas constantes 0 &lt; m &lt; M, donde In es la matriz identidad, entonces 0&#8804; (1 &#8722; t) [det (A)]&#8722;1 + t [det (A + mIn)]&#8722;1 &#8722; [det (A + mtIn)]&#8722;1 &#8804; (1 &#8722; t) [det (A)]&#8722;1 + t [det (B)]&#8722;1 &#8722; [det ((1 &#8722; t) A + tB)]&#8722;1 &#8804; (1 &#8722; t) [det (A)]&#8722;1 + t [det (A + M In)]&#8722;1 &#8722; [det (A + M tIn)]&#8722;1 , para todo t &#8712; [0, 1] .]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Positive definite matrices]]></kwd>
<kwd lng="en"><![CDATA[Determinants]]></kwd>
<kwd lng="en"><![CDATA[Inequalities]]></kwd>
<kwd lng="es"><![CDATA[Matrices definidas positivas]]></kwd>
<kwd lng="es"><![CDATA[Determinantes]]></kwd>
<kwd lng="es"><![CDATA[Desigualdades]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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