# Questions tagged [multivalued-functions]

In Mathematics, set theory, a Multivalued function is defined as a left-total relation (that is, every input is associated with at least one output) in which at least one input is associated with multiple (two or more) outputs.

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### Chebyshev approximation for bivariate function

I read the paper. I am a litte bit confused regarding formulation of Chebyshev approximation for bivariate function(See photo). There is only one integral over variable x. Should it be in formula one ...
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### Representation of concave multivalued/point-to-set maps

Given a point-to-set map $C: X \rightrightarrows Y$ defined by some vector valued-function $\mathbf{g}: X \times Y \to \mathbb{R}^n$ such that $C(x) \doteq \{y \in Y | g_1(x,y), …, g_n(x,y) \geq 0 \}$,...
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### Expressing correspondence via inequalities

Consider a correspondence $C: X \rightrightarrows Y$, that is defined as $C(x) \doteq \{ f_s(x) \mid s \in S \}$ where for all $s \in S$, $f_s$ is a concave function. Can I re-express this ...
1 vote
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### composite function of several variables

recalling functions of single variable ,when writting \begin{gather} (f\circ g) (x)=f(g(x)) \end{gather} this means the $x$ in the domain of $g$ and $g(x)$ in the domain of $f$,that makes the ...
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### Given several values of x, y and z in the relation z=ax+by+c, determine a, b and c

I have inherited a cloud pricing mechanism that essentially uses two variables to derive prices. No-one in the organisation knows the original derivation, but I have about 16 sets of datapoints from ...
1 vote
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### What is the inverse in the complex plane of $e^z + z$?

I want to decide the domain and range of $e^z + z$ and find some properties of its inverse function such as multivalued function. And I guess the domain and range should be whole complex plane ...
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### Solving $C\cos(\sqrt\lambda\theta)+D\sin(\sqrt\lambda\theta)=C\cos(\sqrt\lambda(\theta+2m\pi)) + D\sin(\sqrt\lambda (\theta + 2m\pi))$

I want to solve $$C\cos(\sqrt\lambda \theta) + D\sin(\sqrt\lambda \theta) = C\cos(\sqrt\lambda (\theta + 2m\pi)) + D\sin(\sqrt\lambda (\theta + 2m\pi))$$ The solution must be valid for all $\theta$ in ...
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### Relation of solutions of differential equations around different singular points

In order to clarify my problem, I start with an example $$y'-\frac{1}{2}\left(\frac{1}{x}+\frac{1}{x-1}\right)y=0$$ which has two singular points, $0$ and $1$. The exact solution is not difficult to ...
Suppose I have a complex multivalued function $\log(f(z))$, and I am required to find the principal branch of this function. The method I have learned says that the principal branch of $\log(z)$ is ...