@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-V77DGC4Z-T
  skos:prefLabel "Popoviciu's inequality"@en, "inégalité de Popoviciu"@fr ;
  a skos:Concept ;
  skos:broader psr:-VKBMPHVL-W .

psr:-V4ZPGW2N-C
  skos:prefLabel "Hermite-Hadamard inequality"@en, "inégalité d'Hermite-Hadamard"@fr ;
  a skos:Concept ;
  skos:broader psr:-VKBMPHVL-W .

psr:-QPM2WHP2-7
  skos:prefLabel "fonction logarithmiquement convexe"@fr, "logarithmically convex function"@en ;
  a skos:Concept ;
  skos:broader psr:-VKBMPHVL-W .

psr:-XF0G82RL-K
  skos:prefLabel "fonction Schur-convexe"@fr, "Schur-convex function"@en ;
  a skos:Concept ;
  skos:broader psr:-VKBMPHVL-W .

psr:-WXGNK3BM-N
  skos:prefLabel "Jensen's inequality"@en, "inégalité de Jensen"@fr ;
  a skos:Concept ;
  skos:broader psr:-VKBMPHVL-W .

psr:-ZTD7VMDS-3
  skos:prefLabel "analyse convexe"@fr, "convex analysis"@en ;
  a skos:Concept ;
  skos:narrower psr:-VKBMPHVL-W .

psr:-JZC5LRN2-1
  skos:prefLabel "fonction quasi-convexe"@fr, "quasiconvex function"@en ;
  a skos:Concept ;
  skos:broader psr:-VKBMPHVL-W .

psr: a skos:ConceptScheme .
psr:-VKBMPHVL-W
  skos:definition """En mathématiques, une fonction réelle d'une variable réelle est dite convexe :
         <br/>- si quels que soient deux points <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle A}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>A</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle A}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="A"></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle B}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>B</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle B}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="B"></span> du graphe de la fonction, le segment <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle [AB]}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mo stretchy="false">[</mo>
         <mi>A</mi>
         <mi>B</mi>
         <mo stretchy="false">]</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle [AB]}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13e80b9404482bdbe7fe18d8435b3dd42fd39bb0" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.801ex; height:2.843ex;" alt="{\\\\displaystyle [AB]}"></span> est entièrement situé au-dessus du graphe, c’est-à-dire que la courbe représentative de la fonction se situe toujours en dessous de ses cordes;
<br/>- ou si l'épigraphe de la fonction (l'ensemble des points qui sont au-dessus de son graphe) est un ensemble convexe;
<br/>- ou si vu d'en dessous, le graphe de la fonction est en bosse. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fonction_convexe">https://fr.wikipedia.org/wiki/Fonction_convexe</a>)"""@fr, """In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Convex_function">https://en.wikipedia.org/wiki/Convex_function</a>)"""@en ;
  skos:narrower psr:-JZC5LRN2-1, psr:-V77DGC4Z-T, psr:-XF0G82RL-K, psr:-WXGNK3BM-N, psr:-QPM2WHP2-7, psr:-V4ZPGW2N-C ;
  dc:created "2023-07-13"^^xsd:date ;
  skos:inScheme psr: ;
  skos:prefLabel "convex function"@en, "fonction convexe"@fr ;
  skos:broader psr:-L2BN0W1T-P, psr:-MDFZ99KQ-Q, psr:-ZTD7VMDS-3 ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Fonction_convexe>, <https://en.wikipedia.org/wiki/Convex_function> ;
  dc:modified "2023-07-28"^^xsd:date ;
  a skos:Concept .

psr:-MDFZ99KQ-Q
  skos:prefLabel "fonction numérique"@fr, "real-valued function"@en ;
  a skos:Concept ;
  skos:narrower psr:-VKBMPHVL-W .

psr:-L2BN0W1T-P
  skos:prefLabel "fonction"@fr, "function"@en ;
  a skos:Concept ;
  skos:narrower psr:-VKBMPHVL-W .