data/mathoid/305.mml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="phi left-parenthesis lamda 1 x 1 plus lamda 2 x 2 plus ellipsis plus lamda Subscript n Baseline x Subscript n Baseline right-parenthesis less-than-or-equal-to lamda 1 phi left-parenthesis x 1 right-parenthesis plus lamda 2 phi left-parenthesis x 2 right-parenthesis plus ellipsis plus lamda Subscript n Baseline phi left-parenthesis x Subscript n Baseline right-parenthesis">
<semantics>
<mrow data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-id="83" data-semantic-children="75,80" data-semantic-content="25">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="75" data-semantic-children="0,64" data-semantic-content="74" data-semantic-parent="83">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="75">φ
<!-- φ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="74" data-semantic-parent="75" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="64" data-semantic-children="61" data-semantic-content="1,24" data-semantic-parent="75">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="1" data-semantic-parent="64" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="61" data-semantic-children="58,60,16,63" data-semantic-content="8,15,17" data-semantic-parent="64">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="58" data-semantic-children="4,7" data-semantic-content="57" data-semantic-parent="61">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="4" data-semantic-children="2,3" data-semantic-parent="58">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="4">λ
<!-- λ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="3" data-semantic-parent="4">1</mn>
</mrow>
</msub>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="57" data-semantic-parent="58" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="7" data-semantic-children="5,6" data-semantic-parent="58">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="5" data-semantic-parent="7">x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="6" data-semantic-parent="7">1</mn>
</mrow>
</msub>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="8" data-semantic-parent="61" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="60" data-semantic-children="11,14" data-semantic-content="59" data-semantic-parent="61">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="11" data-semantic-children="9,10" data-semantic-parent="60">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="9" data-semantic-parent="11">λ
<!-- λ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="10" data-semantic-parent="11">2</mn>
</mrow>
</msub>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="59" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="14" data-semantic-children="12,13" data-semantic-parent="60">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="12" data-semantic-parent="14">x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="13" data-semantic-parent="14">2</mn>
</mrow>
</msub>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="15" data-semantic-parent="61" data-semantic-operator="infixop,+">+</mo>
<mo data-semantic-type="punctuation" data-semantic-role="ellipsis" data-semantic-id="16" data-semantic-parent="61">⋯
<!-- ⋯ -->
</mo>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="17" data-semantic-parent="61" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="63" data-semantic-children="20,23" data-semantic-content="62" data-semantic-parent="61">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="20" data-semantic-children="18,19" data-semantic-parent="63">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="18" data-semantic-parent="20">λ
<!-- λ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="20">n</mi>
</mrow>
</msub>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="62" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="23" data-semantic-children="21,22" data-semantic-parent="63">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="23">x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="22" data-semantic-parent="23">n</mi>
</mrow>
</msub>
</mrow>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="24" data-semantic-parent="64" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
<mo data-semantic-type="relation" data-semantic-role="inequality" data-semantic-id="25" data-semantic-parent="83" data-semantic-operator="relseq,≤">≤
<!-- ≤ -->
</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="80" data-semantic-children="77,79,46,82" data-semantic-content="35,45,47" data-semantic-parent="83">
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="77" data-semantic-children="28,73" data-semantic-content="76" data-semantic-parent="80">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="28" data-semantic-children="26,27" data-semantic-parent="77">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="26" data-semantic-parent="28">λ
<!-- λ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="27" data-semantic-parent="28">1</mn>
</mrow>
</msub>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="76" data-semantic-parent="77" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="73" data-semantic-children="29,65" data-semantic-content="72,29" data-semantic-parent="77">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="29" data-semantic-parent="73" data-semantic-operator="appl">φ
<!-- φ -->
</mi>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="72" data-semantic-parent="73" data-semantic-added="true" data-semantic-operator="appl"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="65" data-semantic-children="33" data-semantic-content="30,34" data-semantic-parent="73">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="30" data-semantic-parent="65" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="33" data-semantic-children="31,32" data-semantic-parent="65">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="31" data-semantic-parent="33">x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="32" data-semantic-parent="33">1</mn>
</mrow>
</msub>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="34" data-semantic-parent="65" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="35" data-semantic-parent="80" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="79" data-semantic-children="38,71" data-semantic-content="78" data-semantic-parent="80">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="38" data-semantic-children="36,37" data-semantic-parent="79">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="36" data-semantic-parent="38">λ
<!-- λ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="37" data-semantic-parent="38">2</mn>
</mrow>
</msub>
<mspace width="thinmathspace"/>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="78" data-semantic-parent="79" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="71" data-semantic-children="39,66" data-semantic-content="70,39" data-semantic-parent="79">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="39" data-semantic-parent="71" data-semantic-operator="appl">φ
<!-- φ -->
</mi>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="70" data-semantic-parent="71" data-semantic-added="true" data-semantic-operator="appl"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="66" data-semantic-children="43" data-semantic-content="40,44" data-semantic-parent="71">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="40" data-semantic-parent="66" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="43" data-semantic-children="41,42" data-semantic-parent="66">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="41" data-semantic-parent="43">x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="42" data-semantic-parent="43">2</mn>
</mrow>
</msub>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="44" data-semantic-parent="66" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="45" data-semantic-parent="80" data-semantic-operator="infixop,+">+</mo>
<mo data-semantic-type="punctuation" data-semantic-role="ellipsis" data-semantic-id="46" data-semantic-parent="80">⋯
<!-- ⋯ -->
</mo>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="47" data-semantic-parent="80" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="82" data-semantic-children="50,69" data-semantic-content="81" data-semantic-parent="80">
<msub data-semantic-type="subscript" data-semantic-role="greekletter" data-semantic-id="50" data-semantic-children="48,49" data-semantic-parent="82">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="48" data-semantic-parent="50">λ
<!-- λ -->
</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="49" data-semantic-parent="50">n</mi>
</mrow>
</msub>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="81" data-semantic-parent="82" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="69" data-semantic-children="51,67" data-semantic-content="68,51" data-semantic-parent="82">
<mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="51" data-semantic-parent="69" data-semantic-operator="appl">φ
<!-- φ -->
</mi>
<mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="68" data-semantic-parent="69" data-semantic-added="true" data-semantic-operator="appl"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="67" data-semantic-children="55" data-semantic-content="52,56" data-semantic-parent="69">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="52" data-semantic-parent="67" data-semantic-operator="fenced">(</mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="55" data-semantic-children="53,54" data-semantic-parent="67">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="53" data-semantic-parent="55">x</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="54" data-semantic-parent="55">n</mi>
</mrow>
</msub>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="56" data-semantic-parent="67" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
</mrow>
<annotation encoding="application/x-tex">\varphi (\lambda _{1}x_{1}+\lambda _{2}x_{2}+\cdots +\lambda _{n}x_{n})\leq \lambda _{1}\varphi (x_{1})+\lambda _{2}\,\varphi (x_{2})+\cdots +\lambda _{n}\varphi (x_{n})</annotation>
</semantics>
</math>