Strongly monotone operator

In functional analysis, a set-valued mapping ${\displaystyle A:X\to 2^{X}}$ where X is a real Hilbert space is said to be strongly monotone if

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

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