Question

A new type of convexity related to the exponential function

score 34 · Answer 1 · 2024-03-02 16:49:00

34

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A new type of convexity related to the exponential function

Published on 02 Mar 2024 - 16:49

score 84 · Answer 2 · 2024-03-07 18:40:37

84

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Proving the Increase of $(a+\delta)_m - (a)_m$ Given Decrease of $\frac{(a+\delta)_m}{(a)_m}$.

Published on 07 Mar 2024 - 18:40

score 51 · Answer 3 · 2026-03-25 10:57:07

51

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For a fixed positive definite $A$ anb vector $x$, is $B\mapsto x^T B^{1/2} A B^{1/2} x$ always concave?

Published on 25 Mar 2026 - 10:57

score 25.6k · Answer 4 · 2015-12-11 04:07:34

25.6k

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The minimum value of $ f(x) = | x - 1 | + | x - 2 | + | x - 3 | $ is?

Published on 11 Dec 2015 - 4:07

score 289 · Answer 5 · 2016-06-08 08:52:51

289

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Prove inequality $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}+abc\le \frac52$

Published on 08 Jun 2016 - 8:52

score 247 · Answer 6 · 2017-06-09 16:43:15

247

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What is maximum of $\frac{x^2+y^2+z^2}{xy+xz+yz}$ when $x, y, z \in [1, 2]$?

Published on 09 Jun 2017 - 16:43

score 131 · Answer 7 · 2017-06-16 03:16:33

131

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show this inequality $3^{\frac{n}{4}}\cdot (3^{\frac{1}{4}}-1)^{8-n}\le 1+n$

Published on 16 Jun 2017 - 3:16

score 67 · Answer 8 · 2017-08-07 22:35:13

67

Views

Convexity with conditional probabilities

Published on 07 Aug 2017 - 22:35

score 154 · Answer 9 · 2017-08-19 18:39:53

154

Views

Does strict quasiconvexity imply continuity?

Published on 19 Aug 2017 - 18:39

score 686 · Answer 10 · 2017-10-03 00:28:00

686

Views

Prove that the function f(x) = (x-3)^2 is convex on [1,5]

Published on 03 Oct 2017 - 0:28

score 126 · Answer 11 · 2017-12-23 19:21:05

126

Views

Show that $f$ is convex in $I$ such that $f(\frac{x+y}{2})<\frac{1}{2}(f(x)+f(y))$

Published on 23 Dec 2017 - 19:21

score 61 · Answer 12 · 2020-08-04 19:17:25

61

Views

When does the inequality hold?

Published on 04 Aug 2020 - 19:17

score 157 · Answer 13 · 2020-08-05 11:13:43

157

Views

Little result using RCF theorem and an inequality by Vasile Cirtoaje

Published on 05 Aug 2020 - 11:13

score 71 · Answer 14 · 2020-08-06 22:06:27

71

Views

Question about convexity: how do we prove that $\displaystyle \sum_{i=1}^{k}p_{i}b_{i}\geq\prod_{i=1}^{k}b^{p_{i}}_{i}$?

Published on 06 Aug 2020 - 22:06

score 174 · Answer 15 · 2020-08-13 07:57:03

174

Views

Show that Lambert's function is concave using mid-point concavity

Published on 13 Aug 2020 - 7:57

List Question

A new type of convexity related to the exponential function

Proving the Increase of $(a+\delta)_m - (a)_m$ Given Decrease of $\frac{(a+\delta)_m}{(a)_m}$.

For a fixed positive definite $A$ anb vector $x$, is $B\mapsto x^T B^{1/2} A B^{1/2} x$ always concave?

The minimum value of $ f(x) = | x - 1 | + | x - 2 | + | x - 3 | $ is?

Prove inequality $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}+abc\le \frac52$

What is maximum of $\frac{x^2+y^2+z^2}{xy+xz+yz}$ when $x, y, z \in [1, 2]$?

show this inequality $3^{\frac{n}{4}}\cdot (3^{\frac{1}{4}}-1)^{8-n}\le 1+n$

Convexity with conditional probabilities

Does strict quasiconvexity imply continuity?

Prove that the function f(x) = (x-3)^2 is convex on [1,5]

Show that $f$ is convex in $I$ such that $f(\frac{x+y}{2})<\frac{1}{2}(f(x)+f(y))$

When does the inequality hold?

Little result using RCF theorem and an inequality by Vasile Cirtoaje

Question about convexity: how do we prove that $\displaystyle \sum_{i=1}^{k}p_{i}b_{i}\geq\prod_{i=1}^{k}b^{p_{i}}_{i}$?

Show that Lambert's function is concave using mid-point concavity

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