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Functional

concept 1 articles 17 citations 18 shown relations

$f$ of an arbitrary set $X$ into the set $\mathbb R$ of real numbers or the set $\mathbb C$ of complex numbers. If $X$ is endowed with the structure of a

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A mapping $f$ of an arbitrary set $X$ into the set $\mathbb R$ of real numbers or the set $\mathbb C$ of complex numbers. If $X$ is endowed with the structure of a vector space, a topological space or an ordered set, then there arise the important classes of linear, continuous and monotone functionals, respectively (cf. Linear functional; Continuous functional; Monotone mapping).

References

[1]	A.N. Kolmogorov, S.V. Fomin, "Elements of the theory of functions and functional analysis" , 1–2 , Graylock (1957–1961) (Translated from Russian)

How to Cite This Entry:
Functional. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Functional&oldid=29314

This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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Functionalencyclopedia_of_mathematics

Citations

Linear functionaloutgoing citation Mappingoutgoing citation Vector spaceoutgoing citation Topological spaceoutgoing citation Monotone mappingoutgoing citation Ordered setoutgoing citation Continuous functionaloutgoing citation Lax-Milgram lemmaincoming citation Stochastic programmingincoming citation Hyperplaneincoming citation Functional analysisincoming citation Pontryagin maximum principleincoming citation Bauer-Fike theoremincoming citation Operatorincoming citation Gleason-Kahane-Żelazko theoremincoming citation Babuska-Lax-Milgram theoremincoming citation Binary relationincoming citation

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discussesarticle:eom--functional--c4d878753b -> concept:functionalconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:functional -> concept:linear-functionalconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:functional -> concept:mappingconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:functional -> concept:vector-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:functional -> concept:topological-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:functional -> concept:monotone-mappingconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:functional -> concept:ordered-setconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:functional -> concept:continuous-functionalconfidence: 1.00 - provenance: article link extractionreviewed

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citesconcept:stochastic-programming -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:hyperplane -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:functional-analysis -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:pontryagin-maximum-principle -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:bauer-fike-theorem -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:operator -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:gleason-kahane-zelazko-theorem -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:babuska-lax-milgram-theorem -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:binary-relation -> concept:functionalconfidence: 1.00 - provenance: article backlink extractionreviewed

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