List questions from convexity-inequality

Published on 25 Mar 2026 - 20:41

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Does this strong convexity estimate hold?

Published on 25 Mar 2026 - 22:09

151

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Given four real numbers $a,b,c,d$ so that $1\leq a\leq b\leq c\leq d\leq 3$. Prove that $a^2+b^2+c^2+d^2\leq ab+ac+ad+bc+bd+cd.$

Published on 25 Mar 2026 - 23:42

240

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Does the convex envelope inherit monotonicity properties?

Published on 25 Mar 2026 - 20:35

88

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Expectation of random matrix

Published on 25 Mar 2026 - 20:34

63

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Uniqueness of a point where the chord coincides with the tangent

Published on 25 Mar 2026 - 20:36

138

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How to prove this inequality on given set?

Published on 25 Mar 2026 - 20:34

65

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Why is showing $LHS - RHS \geq 0$ enough to prove convexity of a function?

Published on 25 Mar 2026 - 22:04

129

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General Inequality for Convex Functions

Published on 25 Mar 2026 - 22:09

221

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Prove this refinement of Nesbitt's inequality based on another

Published on 25 Mar 2026 - 23:36

75

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Prove that :$f(a^2)+f(b^2)+f(c^2)\leq f\left(\frac{1}{4}\right)+f\left(\frac{1}{4}\right)+f(0)$ where $f(x)=\sqrt{\frac{1+\sqrt{1+x}}{x^x}}$

Published on 28 Apr 2026 - 16:36

66

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Convexity of $ (a+b)^{1/n}$

Published on 26 Apr 2026 - 1:20

76

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Inequality :$\left(\frac{x}{x+1}\right)^{\tan^2(x)}+\left(\frac{1}{1+3}\right)^{\tan^2(1)}+\left(\frac{3}{x+3}\right)^{\tan^2(3)}>\frac{40}{39}$

Published on 25 Mar 2026 - 23:42

80

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Condition of concavity for a function

Published on 25 Mar 2026 - 20:41

490

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If $f$ is convex, show that $f(x)/x$ is non-decreasing in $x$

Published on 25 Mar 2026 - 20:36

List Question

Limit of a convex function

Does this strong convexity estimate hold?

Given four real numbers $a,b,c,d$ so that $1\leq a\leq b\leq c\leq d\leq 3$. Prove that $a^2+b^2+c^2+d^2\leq ab+ac+ad+bc+bd+cd.$

Does the convex envelope inherit monotonicity properties?

Expectation of random matrix

Uniqueness of a point where the chord coincides with the tangent

How to prove this inequality on given set?

Why is showing $LHS - RHS \geq 0$ enough to prove convexity of a function?

General Inequality for Convex Functions

Prove this refinement of Nesbitt's inequality based on another

Prove that :$f(a^2)+f(b^2)+f(c^2)\leq f\left(\frac{1}{4}\right)+f\left(\frac{1}{4}\right)+f(0)$ where $f(x)=\sqrt{\frac{1+\sqrt{1+x}}{x^x}}$

Convexity of $ (a+b)^{1/n}$

Inequality :$\left(\frac{x}{x+1}\right)^{\tan^2(x)}+\left(\frac{1}{1+3}\right)^{\tan^2(1)}+\left(\frac{3}{x+3}\right)^{\tan^2(3)}>\frac{40}{39}$

Condition of concavity for a function

If $f$ is convex, show that $f(x)/x$ is non-decreasing in $x$

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