List questions from functional-inequalities

Published on 25 Mar 2026 - 11:22

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Is this monotonicity property equivalent to convexity?

Published on 25 Mar 2026 - 11:19

50

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Inequality of functions involving logarithm

Published on 08 May 2020 - 4:28

210

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A variant of Jensen inequality when the function is not everywhere convex

Published on 10 May 2020 - 8:51

39

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Does this "half-line" convexity imply full convexity?

Published on 11 May 2020 - 12:37

90

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Functional inequality $f(x+y)f(x-y)\leq f^2(x)-f^2(y)$

Published on 15 May 2020 - 3:17

36

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Automatic extension of strict convexity

Published on 19 May 2020 - 7:05

196

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Find all positive monotonic functions such that $f(x+y) \le f(x) + f(y)$, $f(0)=0$

Published on 21 May 2020 - 16:35

81

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Functional inequalities involving the condition $\left(\int_0^t f(x)dx\right)^2 \ge \int_0^t f(x)^3dx$

Published on 22 May 2020 - 7:26

54

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Change of Variables Bound on Integral

Published on 04 Jun 2020 - 17:14

201

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$f(xy + x +y) = f(xy) + f(x) + f(y)$ and $f(x)(y - x) + f(y)(x - y) \geq 0$.

Published on 24 Jun 2020 - 6:41

1.4k

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What is the general way of calculating maxima and minima of a given cubic function?

Published on 29 Jun 2020 - 19:06

27

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Proving an energy estimate of $2 \delta \|u\|_{L^2(\Omega)}\|u_t\|_{L^2(\Omega)}+\|b\|_{L^2(\Omega)} \|u_t\|_{L^2(\Omega)}$

Published on 30 Jun 2020 - 9:26

484

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Smallest $c$ such that $f'<cf$ holds for all $f$ such that $f,f',f'',f'''>0$ and $f''' \le f.$

Published on 04 Jul 2020 - 2:02

77

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Strictly increasing function $f: \mathbb{N} \to \mathbb{R}^+$ such that $\lim\limits_{n \to \infty} \frac{f(n)}{n} = 0$ and $f(n)+f(3n) \ge 2f(2n).$

Published on 09 Jul 2020 - 4:32

List Question

Is this property equivalent to convexity?

Is this monotonicity property equivalent to convexity?

Inequality of functions involving logarithm

A variant of Jensen inequality when the function is not everywhere convex

Does this "half-line" convexity imply full convexity?

Functional inequality $f(x+y)f(x-y)\leq f^2(x)-f^2(y)$

Automatic extension of strict convexity

Find all positive monotonic functions such that $f(x+y) \le f(x) + f(y)$, $f(0)=0$

Functional inequalities involving the condition $\left(\int_0^t f(x)dx\right)^2 \ge \int_0^t f(x)^3dx$

Change of Variables Bound on Integral

$f(xy + x +y) = f(xy) + f(x) + f(y)$ and $f(x)(y - x) + f(y)(x - y) \geq 0$.

What is the general way of calculating maxima and minima of a given cubic function?

Proving an energy estimate of $2 \delta \|u\|_{L^2(\Omega)}\|u_t\|_{L^2(\Omega)}+\|b\|_{L^2(\Omega)} \|u_t\|_{L^2(\Omega)}$

Smallest $c$ such that $f'<cf$ holds for all $f$ such that $f,f',f'',f'''>0$ and $f''' \le f.$

Strictly increasing function $f: \mathbb{N} \to \mathbb{R}^+$ such that $\lim\limits_{n \to \infty} \frac{f(n)}{n} = 0$ and $f(n)+f(3n) \ge 2f(2n).$

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