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

\exists \,c>0{\mbox{ s.t. }}\langle Au-Av,u-v\rangle \geq c\|u-v\|^{2}\quad \forall u,v\in X.

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.