Felix' Math Place (Posts about Parseval's identity.) https://math.fontein.de/tag/parsevals-identity.atom 2019-11-17T10:38:30Z Felix Fontein Nikola Inequalities. https://math.fontein.de/2010/02/09/inequalities/ 2010-02-09T06:29:04+01:00 2010-02-09T06:29:04+01:00 Felix Fontein <div><p>Inspired by a <a class="reference external" href="http://twitter.com/ProbFact/statuses/8684799550">tweet</a>, I decided to play a bit with <a class="reference external" href="http://www.graphviz.org/">Graphviz</a> to create a graph on which inequalities imply which ones. Here’s the result:</p> <div style="text-align: center"> <img src="https://math.fontein.de/2010/02/09/inequalities-small.png" width="510" height="210" usemap="https://math.fontein.de/2010/02/09/inequalities/#ineqmap" alt=""> </div> <map name="ineqmap"> <area shape="rect" coords="211,2,274,21" href="https://en.wikipedia.org/wiki/Jensen's_inequality" alt="Jensen's inequality"> <area shape="rect" coords="2,39,75,58" href="https://en.wikipedia.org/wiki/Newton's_inequalities" alt="Newton's inequality"> <area shape="rect" coords="81,39,159,58" href="https://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell_theorem" alt="Rao-Blackwell theorem"> <area shape="rect" coords="169,40,230,58" href="https://en.wikipedia.org/wiki/Log_sum_inequality" alt="Log sum inequality"> <area shape="rect" coords="239,40,330,58" href="https://en.wikipedia.org/wiki/Generalized_mean_inequality" alt="Generalized mean inequality"> <area shape="rect" coords="340,39,508,58" href="https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means#Generalizations" alt="Inequality of arithmetic and geometric mean"> <area shape="rect" coords="14,77,84,96" href="https://en.wikipedia.org/wiki/Muirhead's_inequality" alt="Muirhead's inequality"> <area shape="rect" coords="93,77,165,95" href="https://en.wikipedia.org/wiki/Maclaurin's_inequality" alt="Maclaurin's inequality"> <area shape="rect" coords="174,77,232,96" href="https://en.wikipedia.org/wiki/Gibb's_inequality" alt="Gibb's inequality"> <area shape="rect" coords="245,77,310,95" href="https://en.wikipedia.org/wiki/Pythagorean_means" alt="Pythagorean means"> <area shape="rect" coords="372,78,476,95" href="https://en.wikipedia.org/wiki/Young's_inequality" alt="Young's inequality"> <area shape="rect" coords="193,114,332,133" href="https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means" alt="Inequality of arithmetic and geometric means"> <area shape="rect" coords="391,114,457,133" href="https://en.wikipedia.org/wiki/H%C3%B6lder's_inequality" alt="Hölder's inequality"> <area shape="rect" coords="162,152,223,171" href="https://en.wikipedia.org/wiki/Parseval's_identity" alt="Parseval's inequality"> <area shape="rect" coords="232,152,294,170" href="https://en.wikipedia.org/wiki/Mahler's_inequality" alt="Mahler's inequality"> <area shape="rect" coords="304,152,391,171" href="https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality" alt="Cauchy-Schwarz inequality"> <area shape="rect" coords="400,152,475,171" href="https://en.wikipedia.org/wiki/Minkowski's_inequality" alt="Minkowski's inequality"> <area shape="rect" coords="249,189,311,208" href="https://en.wikipedia.org/wiki/Bessel's_inequality" alt="Bessel's inequality"> <area shape="rect" coords="362,190,423,208" href="https://en.wikipedia.org/wiki/Triangle_inequality" alt="Triangle inequality"> </map><p>Click <a class="reference external" href="https://math.fontein.de/2010/02/09/inequalities-large.png">here</a> to obtain a larger version. Click any box on the image to obtain the <a class="reference external" href="https://en.wikipedia.org/wiki/Main_Page">Wikipedia</a> page on the inequality.</p></div>