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Multiple-Valued Function

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Multiple-Valued Function

 

a function that takes on several values for the same value of the argument. Multiple-valued functions arise when we invert single-valued functions whose values repeat. Thus, the function x2 takes on every positive value twice (for values of the argument differing only in sign); its inverse is the two-valued function Multiple-valued Function The function sin x takes on each of its values an infinite number of times; its inverse is the infinite-valued function arcs in x. Multiple-valued functions play an important role in the theory of analytic functions of a complex variable. In the complex domain, Multiple-valued Function has n values for any z ≠ 0, and f(z) = ln z, when z ≠ 0, has an infinite number of values.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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References in periodicals archive
A multivalued function F : I [right arrow] cc(I) is increasing (resp., strictly increasing) if for every x,y [member of] I with x < y, we have max F(x) [less than or equal to] min F(y) (resp., max F(x) < min F(y)) (cf.
which is a modified version of (2), for the piecewise Lipschitzian multivalued functions defined in [4].
where F(I) is the set of all multivalued functions F : I [right arrow] cc(I).
According to above the argument, F [member of] USI(I) was divided into two cases in [4]: one is unblended multivalued functions; the other is blended ones.
Since functions in USI(I) are strictly increasing, it suffices to discuss multivalued functions F in USI(I) which satisfy either min F(x) > x for all x [member of] int I or max F(x) < x for all x [member of] int I.
On the Blended Solutions of Polynomial-Like Iterative Equation with Multivalued Functions
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