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Results tagged with fixed-point-theorems
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user 6634
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
The property does not hold as stated. Consider the case $u=(\frac{1}{2},\dots,\frac{1}{2}), A=\frac{1}{4}I,$ and $Q(x)_i = \frac{1}{4}x_i^2$. Then $\Phi$ maps $(x_1,\dots,x_n)$ to $\frac{1}{4}(x_1^2+x …
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