List questions from functional-inequalities

Published on 21 Mar 2026 - 21:17

119

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How to minimise this expression?

Published on 22 Mar 2026 - 3:28

530

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Prove an integral inequality ($e^{\alpha x}u(x) \le e^{\alpha y}u(y) + \int_y^x e^{\alpha \xi} f(\xi) d\xi$) under certain hypotheses

Published on 22 Mar 2026 - 11:41

96

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When does $g(x) > 0$ and $0 \le f'(x) \le g(x)f(x)$ imply that $f(x) = 0$?

Published on 22 Mar 2026 - 6:25

139

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Obtain definition of convex function

Published on 22 Mar 2026 - 11:38

78

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Anyone can help me prove an exponential inequality?

Published on 22 Mar 2026 - 0:37

107

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Show that $x^e\le e^x$ for all $x\gt 0$ and $x \in \mathbb {R}$

Published on 22 Mar 2026 - 7:20

81

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$g : [0,1]\to\Bbb R$ is a concave function with $g(0) =0$ and $g(1)= \beta$. Show that $g(z) \geq \beta z$, $z \in [0,1]$.

Published on 21 Mar 2026 - 23:53

389

Views

Integral inequality involving the derivative

Published on 22 Mar 2026 - 14:01

73

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Is there analytic solution to this functional problem?

Published on 22 Mar 2026 - 10:10

128

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Weird norm of the functional

Published on 21 Mar 2026 - 19:42

749

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Does the Gagliardo–Nirenberg interpolation inequality also hold for surfaces?

Published on 22 Mar 2026 - 3:01

152

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Nonlinear differential inequalities

Published on 21 Mar 2026 - 20:29

53

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How to solve that logarithmic inequality?

Published on 21 Mar 2026 - 17:16

56

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Non-polynomial solutions for a functional inequality

Published on 22 Mar 2026 - 8:28

List Question

How can I prove $\log_2{(1+x)} \geq {x}$ for $0<x<1$

How to minimise this expression?

Prove an integral inequality ($e^{\alpha x}u(x) \le e^{\alpha y}u(y) + \int_y^x e^{\alpha \xi} f(\xi) d\xi$) under certain hypotheses

When does $g(x) > 0$ and $0 \le f'(x) \le g(x)f(x)$ imply that $f(x) = 0$?

Obtain definition of convex function

Anyone can help me prove an exponential inequality?

Show that $x^e\le e^x$ for all $x\gt 0$ and $x \in \mathbb {R}$

$g : [0,1]\to\Bbb R$ is a concave function with $g(0) =0$ and $g(1)= \beta$. Show that $g(z) \geq \beta z$, $z \in [0,1]$.

Integral inequality involving the derivative

Is there analytic solution to this functional problem?

Weird norm of the functional

Does the Gagliardo–Nirenberg interpolation inequality also hold for surfaces?

Nonlinear differential inequalities

How to solve that logarithmic inequality?

Non-polynomial solutions for a functional inequality

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