Strongly monotone

In functional analysis, an operator ${\displaystyle A:X\to X^{*}}$ where X is a real Hilbert space is said to be strongly monotone if

${\displaystyle \exists \,c>0{\mbox{ s.t. }}\langle Au-Av,u-v\rangle \geq c\|u-v\|^{2}\quad \forall u,v\in X.}$

This is analogous to the notion of strictly increasing for scalar-valued functions of one scalar argument.

For more information, see coercivity