Multivalued function
Generalized mathematical function / From Wikipedia, the free encyclopedia
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In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least one point in its domain.[1] It is a set-valued function with additional properties depending on context. The terms multifunction and many-valued function are sometimes also used.
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This article is about multivalued functions as they are considered in mathematical analysis. For set-valued functions as considered in variational analysis, see set-valued function.
Not to be confused with Multivariate function.
A multivalued function of sets f : X → Y is a subset
Write f(x) for the set of those y ∈ Y with (x,y) ∈ Γf. If f is an ordinary function, it is a multivalued function by taking its graph
- :\ x\in X\}.}
They are called single-valued functions to distinguish them.