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A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.
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fixed points of system of quadratic equations
Let $\Phi: R^n \to R^n$ satisfy
$\Phi(x)=u+Ax+Q(x)$, with $x=(x_1, x_2,\ldots, x_n) \in R^n$. $u$ is a given positive vector, $A$ non negative matrix, and $Q(x)$ quadratic mapping with
$Q(x)_i=x_i(k …