Strongly monotone

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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. } (Au-Av | u-v)\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.

[edit] See also

[edit] Referencess

  • Ziedler. Applied Functional Analysis (AMS 108) p. 173
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