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Results tagged with ca.classical-analysis-and-odes
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user 11512
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
0
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An inequality on concave functions
That $\log \circ f$ is concave follows from concavity of $\log$ and $f$ because $f$ is non-decreasing. I do not see how you could put positivity to use here.
- 446
0
votes
An inequality on concave functions
We want
$$f(x)f(stx)\le f(sx)f(tx)$$
for concave non-decreasing functions with $f(0) = 0$. Since we require this for every $x$ and $f$ we can assume $x = 1$, because our claim is invariant w.r.t scali …
- 446