Strongly monotone operator
From HandWiki
In functional analysis, a set-valued mapping [math]\displaystyle{ A:X\to 2^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 u-v , x-y \rangle\geq c \|x-y\|^2 \quad \forall x,y\in X, u\in Ax, v\in Ay. }[/math]
This is analogous to the notion of strictly increasing for scalar-valued functions of one scalar argument.
See also
References
- Zeidler. Applied Functional Analysis (AMS 108) p. 173
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