Strongly monotone operator

Template:Short description 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

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

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
• Template:Bauschke Combettes Convex Analysis and Monotone Operator Theory in Hilbert Spaces 2nd ed 2017

Template:Mathanalysis-stub