Timeline for Is the inequality $\sum_{i} p_i \frac{a_i}{b_i} \leq \frac{\sum_{i} p_i a_i}{\sum_{i} p_i b_i}$ true?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2023 at 16:00 | vote | accept | Funmecat | ||
| Jun 15, 2023 at 13:14 | comment | added | Fedor Petrov | @DenisSerre certainly I do (and apart of that just suggest a suitable parametrization: for $y=ax+b$ this is less transparent). | |
| Jun 15, 2023 at 12:15 | comment | added | Denis Serre | @FedorPetrov. Aren't you reformulating the definition of convexity ? :) | |
| Jun 15, 2023 at 10:25 | comment | added | Fedor Petrov | For what it worth, restricting to the lines $x=ay+b$ makes the convexity question of these functions pretty clear. | |
| Jun 15, 2023 at 7:59 | comment | added | Denis Serre | @YaakovBaruch. The convexity of $x^2/y$ over ${\mathbb R}\times(0,+\infty)$ is well-known in mathematical fluid dynamics, because of the kinetic energy, written in terms of the linear momentum and the mass density. | |
| Jun 15, 2023 at 7:57 | history | edited | Denis Serre | CC BY-SA 4.0 |
added 36 characters in body
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| Jun 15, 2023 at 7:56 | comment | added | Yaakov Baruch | Nice answer. Without graphing them I never would have thought that $x^2/y$ is convex while $x/y$ isn't! | |
| Jun 15, 2023 at 7:49 | comment | added | Denis Serre | @YaakovBaruch. Yes I do. | |
| Jun 15, 2023 at 7:44 | comment | added | Yaakov Baruch | By $f({\mathbb E}[a,b])$ you mean $f({\mathbb E}[a],{\mathbb E}[b])$? | |
| Jun 15, 2023 at 7:24 | history | answered | Denis Serre | CC BY-SA 4.0 |