List questions from functional-inequalities

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Is this monotonicity property equivalent to convexity?

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51

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Inequality of functions involving logarithm

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

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40

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

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91

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

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37

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Automatic extension of strict convexity

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197

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

Published on 25 Mar 2026 - 18:49

82

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

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55

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Change of Variables Bound on Integral

Published on 25 Mar 2026 - 18:49

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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 25 Mar 2026 - 18:50

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

Published on 25 Mar 2026 - 18:49

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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 25 Mar 2026 - 18:49

485

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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 25 Mar 2026 - 18:50

78

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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 25 Mar 2026 - 18:49

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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