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

$\mathrm{\exists }c>0\text{ s.t. }⟨Au-Av,u-v⟩\ge c\Vert u-v{\Vert }^2\mathrm{\forall }u,v\in X.$

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

For more information, see coercivity

See also

• Monotonic function

References

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