= Uniqueness for a strongly monotone variational inequality
{title2=$\langle Au,v-u\rangle\ge0\quad(v\in K)$}
Let $K$ be a <convex set> in a real <Banach space>, and let $A:K\to X^*$ be a <strongly monotone operator>. If $u,w\in K$ both satisfy the displayed <variational inequality>, testing with $v=w$ and $v=u$ respectively and adding yields $\langle Au-Aw,u-w\rangle\le0$. Strong monotonicity gives $m\|u-w\|^2\le0$, hence $u=w$. This proves uniqueness whenever a solution exists.
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