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Results tagged with fixed-point-theorems
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user 5963
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.
5
votes
Reference request: an elementary proof of Brouwer fixed-point theorem.
Could one of these two be what you're looking for?
J. Milnor, Analytic proofs of the “hairy ball theorem” and the Brouwer fixed-point theorem, Amer. Math. Monthly 85 (1978), no. 7, 521–524. MR MR505 …
- 8,501
8
votes
Accepted
Is the Binomial Expectation of Convex Function Convex in p?
Here is my original answer (see below for a better one):
Writing down
\[
g(p) = \sum_{k=0}^n h(k)\binom{n}{k}p^k(1-p)^{n-k}
\]
and differentiating twice gives
\[
g''(p) = \sum_{k=0}^n h(k)\binom{n} …
- 8,501