Question

Does there exist a nontrivial cumulative distribution function $F$ on $\mathbb{R}_+$ for which $(F^2)'= (F')^{\ast k}$ for some $k > 0$?

score 83 · Answer 1 · 2026-03-29 03:36:08

83

Views

Does there exist a nontrivial cumulative distribution function $F$ on $\mathbb{R}_+$ for which $(F^2)'= (F')^{\ast k}$ for some $k > 0$?

Published on 29 Mar 2026 - 3:36

score 104 · Answer 2 · 2026-04-05 22:29:49

104

Views

Can the Euler-Lagrange equations be derived from a variation over a time of order $dt$ rather than $t$?

Published on 05 Apr 2026 - 22:29

score 190 · Answer 3 · 2014-03-02 12:33:39

190

Views

Find $f(10)$ in the functional equation $f(f(n))=3n$

Published on 02 Mar 2014 - 12:33

score 364 · Answer 4 · 2014-03-04 19:26:51

$\forall x\in\mathbb R$, $|x|\neq 1$ it is known that $f\left(\frac{x-3}{x+1}\right)+f\left(\frac{3+x}{1-x}\right)=x$. Find $f(x)$.

score 199 · Answer 5 · 2014-03-05 14:40:23

199

Views

Does there exist a continuous function $f\colon \Bbb R\rightarrow \Bbb R$ such that $f(f(x))=-x$ for all $x\in\Bbb R$?

Published on 05 Mar 2014 - 14:40

score 143 · Answer 6 · 2014-03-05 20:38:54

143

Views

A scaling functional equation

Published on 05 Mar 2014 - 20:38

score 52 · Answer 7 · 2014-03-06 10:16:00

52

Views

Solution to a general scaling problem $G(\lambda z)=\frac{G(z)}{\gamma z^n}$

Published on 06 Mar 2014 - 10:16

score 4.3k · Answer 8 · 2014-03-07 05:42:22

4.3k

Views

Functional Equation : If $(x-y)f(x+y) -(x+y)f(x-y) =4xy(x^2-y^2)$ for all x,y find f(x).

Published on 07 Mar 2014 - 5:42

score 200 · Answer 9 · 2014-03-07 18:12:52

200

Views

Functional equation $xf(y)+yf(x)=f(x+y)^2-f\left(x^2\right)-f\left(y^2\right)$

Published on 07 Mar 2014 - 18:12

score 196 · Answer 10 · 2014-03-08 01:31:17

196

Views

Solving the functional equation $f\left(y^2f(x)+x^2f(y)\right)=xy\big(f(x)+f(y)\big)$

Published on 08 Mar 2014 - 1:31

score 129 · Answer 11 · 2014-03-08 07:10:58

129

Views

Solve functional equation

Published on 08 Mar 2014 - 7:10

score 793 · Answer 12 · 2017-04-10 13:29:55

793

Views

Showing that $f(x)=\frac x{x+1}$ is the unique function satisfying $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\big(f(x)\big)$

Published on 10 Apr 2017 - 13:29

score 695 · Answer 13 · 2026-03-27 00:05:27

695

Views

Find all continuous functions such that $f(x)f(2x)\dots f(nx) \le an^k$

Published on 27 Mar 2026 - 0:05

score 67 · Answer 14 · 2017-04-13 07:15:47

67

Views

Limit of a functional equation

Published on 13 Apr 2017 - 7:15

score 31 · Answer 15 · 2017-04-13 14:29:18

31

Views

Is Jensens equation when F(0)=0 and F(1)=1 identical to cauchy functional equation in the rational, non continous case

Published on 13 Apr 2017 - 14:29

List Question

Does there exist a nontrivial cumulative distribution function $F$ on $\mathbb{R}_+$ for which $(F^2)'= (F')^{\ast k}$ for some $k > 0$?

Can the Euler-Lagrange equations be derived from a variation over a time of order $dt$ rather than $t$?

Find $f(10)$ in the functional equation $f(f(n))=3n$

$\forall x\in\mathbb R$, $|x|\neq 1$ it is known that $f\left(\frac{x-3}{x+1}\right)+f\left(\frac{3+x}{1-x}\right)=x$. Find $f(x)$.

Does there exist a continuous function $f\colon \Bbb R\rightarrow \Bbb R$ such that $f(f(x))=-x$ for all $x\in\Bbb R$?

A scaling functional equation

Solution to a general scaling problem $G(\lambda z)=\frac{G(z)}{\gamma z^n}$

Functional Equation : If $(x-y)f(x+y) -(x+y)f(x-y) =4xy(x^2-y^2)$ for all x,y find f(x).

Functional equation $xf(y)+yf(x)=f(x+y)^2-f\left(x^2\right)-f\left(y^2\right)$

Solving the functional equation $f\left(y^2f(x)+x^2f(y)\right)=xy\big(f(x)+f(y)\big)$

Solve functional equation

Showing that $f(x)=\frac x{x+1}$ is the unique function satisfying $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\big(f(x)\big)$

Find all continuous functions such that $f(x)f(2x)\dots f(nx) \le an^k$

Limit of a functional equation

Is Jensens equation when F(0)=0 and F(1)=1 identical to cauchy functional equation in the rational, non continous case

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