List questions from monotone-functions

Published on 01 Jun 2019 - 22:42

498

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Optimize concave function divided by a linear function

Published on 08 Jun 2019 - 8:02

203

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$a_k = \sum\limits_{i=1}^{k-1}a_i \left(\frac{1}{k-i}-\frac{1}{k-i+1}\right)$ and $a_1 = 1$, prove the series is decreasing?

Published on 09 Jun 2019 - 1:59

29

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Non-increasing continuous function with zero initial value

Published on 13 Jun 2019 - 7:02

391

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Generalizing a theorem from real analysis regarding strictly increasing functions

Published on 21 Jun 2019 - 5:34

86

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An integral inequality for a real-valued differentiable monotone function on $[0,1]$

Published on 25 Mar 2026 - 20:34

174

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If $f : \mathbb{R}^n \to \Bbb R$ is monotone over all lines, can it be written as $h \circ l$ where $h$ is monotone and $l$ is a linear form?

Published on 28 Jun 2019 - 14:23

41

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Monotonic function

Published on 03 Jul 2019 - 7:59

75

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Monotonicity of $y(x)=1+xy(x)^m$

Published on 03 Jul 2019 - 13:29

627

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Inverting a monotone polynomial

Published on 08 Jul 2019 - 8:55

100

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Monotonicity of $\int^x_0\frac{F(y)}{F(x)}dy$

Published on 09 Jul 2019 - 15:42

136

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Find $f:\mathbb{Q} \rightarrow \mathbb{R}$ where the mean value theorem fails

Published on 10 Jul 2019 - 13:20

91

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Is $f: (0,\infty ) \to \mathbb{R}$ , $f(x):=\ln(x)+e^x$ injective?

Published on 13 Jul 2019 - 14:43

753

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If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing

Published on 13 Jul 2019 - 15:47

67

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Must $g(x)$ be a monotone function?

Published on 20 Jul 2019 - 12:48

List Question

prove increasing of this inequality on this interval?

Optimize concave function divided by a linear function

$a_k = \sum\limits_{i=1}^{k-1}a_i \left(\frac{1}{k-i}-\frac{1}{k-i+1}\right)$ and $a_1 = 1$, prove the series is decreasing?

Non-increasing continuous function with zero initial value

Generalizing a theorem from real analysis regarding strictly increasing functions

An integral inequality for a real-valued differentiable monotone function on $[0,1]$

If $f : \mathbb{R}^n \to \Bbb R$ is monotone over all lines, can it be written as $h \circ l$ where $h$ is monotone and $l$ is a linear form?

Monotonic function

Monotonicity of $y(x)=1+xy(x)^m$

Inverting a monotone polynomial

Monotonicity of $\int^x_0\frac{F(y)}{F(x)}dy$

Find $f:\mathbb{Q} \rightarrow \mathbb{R}$ where the mean value theorem fails

Is $f: (0,\infty ) \to \mathbb{R}$ , $f(x):=\ln(x)+e^x$ injective?

If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing

Must $g(x)$ be a monotone function?

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