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Functional (mathematics) - Wikipedia

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In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). This article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations. The first concept, which is more modern and abstract, is discussed in detail in a separate article, under the name linear form. The third concept is detailed in the computer science article on higher-order functions. In the case where the space 𝑋 is a space of functions, the functional is a "function of a function",[6] and some older authors actually define the term "functional" to mean "function of a function". However, the fact that 𝑋 is a space of functions is not mathematically essential, so this older definition is no longer prevalent.[citation needed] The term originates from the calculus of variations, where one searches for a function that minimizes (or maximizes) a given functional.

Functional (mathematics) - Wikipedia Jump to content From Wikipedia, the free encyclopedia Types of mappings in mathematics For other uses, see Functional . Not to be confused with functional notation . This article needs more citations . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . Find sources: "Functional" mathematics – news · newspapers · books · scholar · JSTOR ( September 2023 ) ( Learn how and when to remove this message ) The arc length functional has as its domain the vector space of rectifiable curves –

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