Strongly monotone operator explained

In functional analysis, a set-valued mapping

A:X\to 2 ^{X} where X is a real Hilbert space is said to be strongly monotone if\existsc> 0 s.t. \langle u - v , x - y \rangle\geq c \|x - y\| ^{2} \forall x,y\in X, u\in Ax, v\in Ay. 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