Strongly monotone

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

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

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

See also

• Monotonic function

References

• Zeidler. Applied Functional Analysis (AMS 108) p. 173