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Numerical algorithms for problems in analysis and algebra, scientific computation

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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.
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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 …
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Numerical analysis of parabolic obstacle problem

There's an overview of available schemes in chapter III of Roland Glowinski, MR 737005 Numerical methods for nonlinear variational problems, ISBN: 0-387-12434-9. (of which there is also reprint from …
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