<?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>0121-1935</journal-id>
<journal-title><![CDATA[Revista de Ciencias]]></journal-title>
<abbrev-journal-title><![CDATA[rev. cienc.]]></abbrev-journal-title>
<issn>0121-1935</issn>
<publisher>
<publisher-name><![CDATA[Universidad del Valle]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-19352018000100045</article-id>
<article-id pub-id-type="doi">10.25100/rc.v22i1.7100</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Multivalued Usco Functions and Stegall Spaces]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Narváez]]></surname>
<given-names><![CDATA[Diana Ximena]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Valle Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>22</volume>
<numero>1</numero>
<fpage>45</fpage>
<lpage>71</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-19352018000100045&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-19352018000100045&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-19352018000100045&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this article we consider the study of the &#119866; -differentiability and F-ifferentiability for convex functions, not only in the general context of topological vector spaces (&#119905;. &#119907;. &#119904;.), but also in the context of Banach spaces. We study a special class of Banach spaces named Stegall spaces, denoted by &#120190;, which is located between the Asplund &#119865;-spaces and Asplund &#119866;-spaces (&#119970;-Asplund). We present a self-contained proof of the Stegall theorem, without appealing to the huge number of references required in some proofs available in the classical literature (1). This requires a thorough study of a very special type of multivalued functions between Banach spaces known as usco multi-functions.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Bornology]]></kwd>
<kwd lng="en"><![CDATA[usco mapping]]></kwd>
<kwd lng="en"><![CDATA[subdifferential]]></kwd>
<kwd lng="en"><![CDATA[Asplund spaces]]></kwd>
<kwd lng="en"><![CDATA[Stegall spaces]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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</back>
</article>
