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The reasoning is based on the Schauder fixed point theorem.
Some are fixed point, some floating.
This was also required to prevent fixed point overflow.
Hence, has fixed point and fixed point.
Therefore, has fixed point and fixed point.
Generalized fixed point theorems.
(Brouwer fixed point theorem).
(Banach fixed point theorem).
(Browder fixed point theorem).
(Kakutani fixed point theorem).
By Schauder fixed point theorem, has a fixed point.
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