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

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