Strongly monotone

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

[math]\displaystyle{ \exists\,c\gt 0 \mbox{ s.t. } \langle Au-Av , u-v \rangle\geq c \|u-v\|^2 \quad \forall u,v\in X. }[/math]

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

For more information, see coercivity

See also

• Monotonic function

References

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