Strongly monotone

Strongly monotone

In functional analysis, an operator A:X o 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,vin X.This is analogous to the notion of strictly increasing for scalar-valued functions of one scalar argument.

ee also

* Monotonic function

Referencess

* Ziedler. "Applied Functional Analysis" (AMS 108) p. 173


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Monotone preferences — In economics, an agent s preferences are said to be weakly monotonic if, given a consumption bundle x, the agent prefers all consumption bundles y that have more of every good. That is, implies . An agent s preferences are said to be strongly… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Energetic space — In mathematics, more precisely in functional analysis, an energetic space is, intuitively, a subspace of a given real Hilbert space equipped with a new energetic inner product. The motivation for the name comes from physics, as in many physical… …   Wikipedia

  • New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …   Wikipedia

  • Monotonically normal space — In mathematics, a monotonically normal space is a particular kind of normal space, with some special characteristics, and is such that it is hereditarily normal, and any two separated subsets are strongly separated. They are defined in terms of a …   Wikipedia

  • Clique problem — The brute force algorithm finds a 4 clique in this 7 vertex graph (the complement of the 7 vertex path graph) by systematically checking all C(7,4)=35 4 vertex subgraphs for completeness. In computer science, the clique problem refers to any of… …   Wikipedia

  • Glossary of order theory — This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources might be …   Wikipedia

  • Circuit complexity — In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of Boolean circuits that compute them. A Boolean circuit with n input bits …   Wikipedia

  • 2-satisfiability — In computer science, 2 satisfiability (abbreviated as 2 SAT or just 2SAT) is the problem of determining whether a collection of two valued (Boolean or binary) variables with constraints on pairs of variables can be assigned values satisfying all… …   Wikipedia

  • painting, Western — ▪ art Introduction       history of Western painting from its beginnings in prehistoric times to the present.       Painting, the execution of forms and shapes on a surface by means of pigment (but see also drawing for discussion of depictions in …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”