List questions from convexity-inequality

Published on 01 Apr 2026 - 15:12

132

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Let $a$, $b$, $c$ be three positive real numbers contained in the interval [0,1].

Published on 25 Mar 2026 - 11:20

138

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Strong convexity inequality implied by a second derivative which is positive definite outside a convex set

Published on 11 Apr 2026 - 17:05

130

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Prove that the function cannot be strictly concave on $[0,1]$

Published on 25 Mar 2026 - 11:17

163

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One-sided derivatives - convexity

Published on 01 Apr 2026 - 11:28

97

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Is this property equivalent to convexity?

Published on 25 Mar 2026 - 11:22

280

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Is this monotonicity property equivalent to convexity?

Published on 25 Mar 2026 - 11:19

310

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How to prove that the expectation of a random vector lies in the convex hull of its support?

Published on 25 Mar 2026 - 11:24

77

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We cannot make a function convex by decreasing its value

Published on 25 Mar 2026 - 11:17

109

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Prove that $x^2+y^2-\sqrt{2}xy < 4$ provided $1\le x,y \le \frac{5}{2}$.

Published on 25 Mar 2026 - 11:21

232

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A Hamiltonian inequality using uniform convexity and Taylor's formula (Evans PDE, §3.3.3, Lemma 4, (36))

Published on 25 Mar 2026 - 11:03

111

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Does strict convexity plus asymptotic affinity imply bounded mean?

Published on 25 Mar 2026 - 11:19

68

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Prove that the tangent $A$ and $B$ are perpendicular .

Published on 25 Mar 2026 - 11:19

119

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Does convexity around a point imply the function is above the tangent at that point?

Published on 25 Mar 2026 - 11:20

338

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minimizing a concave function

Published on 01 Apr 2026 - 3:12

List Question

How to prove the concavity of this function?

Let $a$, $b$, $c$ be three positive real numbers contained in the interval [0,1].

Strong convexity inequality implied by a second derivative which is positive definite outside a convex set

Prove that the function cannot be strictly concave on $[0,1]$

One-sided derivatives - convexity

Is this property equivalent to convexity?

Is this monotonicity property equivalent to convexity?

How to prove that the expectation of a random vector lies in the convex hull of its support?

We cannot make a function convex by decreasing its value

Prove that $x^2+y^2-\sqrt{2}xy < 4$ provided $1\le x,y \le \frac{5}{2}$.

A Hamiltonian inequality using uniform convexity and Taylor's formula (Evans PDE, §3.3.3, Lemma 4, (36))

Does strict convexity plus asymptotic affinity imply bounded mean?

Prove that the tangent $A$ and $B$ are perpendicular .

Does convexity around a point imply the function is above the tangent at that point?

minimizing a concave function

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