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6
votes
Accepted
Inf of a mutivariate function
This is discussed briefly as a generalization of Shapiro's cyclic sum
inequality by J. Michael Steele in his book
The Cauchy-Schwarz Master Class.
He remarks that (1.) holds for $n\ge25$ and refers to …
15
votes
Is it true that all the "irrational power" functions are almost polynomial ?
There is an "iterated" version of the mean value theorem which states that for
a smooth enough function $f$ on an interval that $\Delta^k f(x)=f^{(k)}(\xi)$
where $\xi$ is between $x$ and $x+k$. This …