Strongly monotone operator

In functional analysis, a set-valued mapping where X is a real Hilbert space is said to be strongly monotone if . This is analogous to the notion of strictly increasing for scalar-valued functions of one scalar argument.

Equivalently, a binary relation is strongly monotone if .

A function is strongly monotone if .

See also Monotonic function

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