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Reference.org
Functional square root
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a functional square root (sometimes called a half iterate) is a <a href="/facts/Square_root/AfrzfBdQ">square root</a> of a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> with respect to the operation of <a href="/facts/Function_composition/r5Pvnmth">function composition</a>. In other words, a functional square root of a function <i>g</i> is a function <i>f</i> satisfying <i>f</i>(<i>f</i>(<i>x</i>)) = <i>g</i>(<i>x</i>) <a href="/facts/For_all/agNmvJKN">for all</a> <i>x</i>. </p>