Category:Definitions/Functionals
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This category contains definitions related to Functionals.
Related results can be found in Category:Functionals.
Definition
A functional is a mapping:
Real Functional
Let $J: S \to \R$ be a mapping from $S$ to the real numbers $\R$:
- $\forall y \in S: \exists x \in \R: J \sqbrk y = x$
Then $J: S \to \R$ is known as a (real) functional, denoted by $J \sqbrk y$.
That is, a (real) functional is a real-valued function whose arguments are themselves mappings.
Examples
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: functional
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: functional
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Definitions/Functionals"
The following 3 pages are in this category, out of 3 total.