= Strongly monotone operator
{title2=$\langle A(u)-A(v),u-v\rangle\ge m\|u-v\|^2,\quad m>0$}
A map from a subset of a real <Banach space> to its <continuous dual space> is strongly monotone if the displayed inequality holds for every pair in its domain, with one constant $m>0$. The brackets denote the <dual pairing>. This implies strict <monotonicity> for distinct arguments. Fixing $v=u_0$ and applying the dual norm inequality gives $\langle A(u),u-u_0\rangle\ge m\|u-u_0\|^2-\|A(u_0)\|\|u-u_0\|$, so it is a <nonlinear coercive operator> with respect to $u_0$.
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