Timeline for Concave functions of different behaviour in the neighbourhood of $0$ from the Shannon function
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2023 at 11:49 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
a minor typo
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| Mar 19, 2013 at 10:47 | comment | added | user27381 | Ok. in this case we are able to show that [\limsup_{z\to 0^+}\frac{g(x)}{-x\ln x}=\limsup_{n\to\infty}\frac{g(M^{-n})}{M^{-n}\ln M^{-n}}] for any $M>1$ and the same is true for the lower limit | |
| Jan 17, 2013 at 14:41 | comment | added | user27381 | Another problem which is connected with this limit - is the following equality true for $g$, which fullfills the above assumptions [ \limsup_{x\to 0^+}\frac{g(x)}{-x\ln x}= \sup_{M\in\mathbb{N}}\limsup_{n\to\infty}\frac{g(M^{-n})}{M^{-n}\ln M^{-n}}.] The crucial assuption seems to be concavity of $g$ (of course if the equality is true) | |
| Jan 17, 2013 at 14:34 | comment | added | user27381 | Pietro, thank You very much for suggestion - it has solved many problems | |
| Nov 29, 2012 at 9:43 | history | edited | Pietro Majer | CC BY-SA 3.0 |
deleted 14 characters in body; edited body
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| Nov 29, 2012 at 9:32 | history | answered | Pietro Majer | CC BY-SA 3.0 |