Question

Multivariate polynomial functional equation

score 295 · Answer 1 · 2026-03-25 04:35:04

295

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Multivariate polynomial functional equation

Published on 25 Mar 2026 - 4:35

score 104 · Answer 2 · 2019-04-09 18:20:47

104

Views

Find all real functions such that $(x + 1)f(xf(y)) = xf(y(x + 1))$

Published on 09 Apr 2019 - 18:20

score 197 · Answer 3 · 2019-04-10 08:41:26

197

Views

Find all functions $f$ for which $f(x-y) = f(x) + f(y) - 2xy$ for all real numbers $x$ and $y$.

Published on 10 Apr 2019 - 8:41

score 50 · Answer 4 · 2026-03-25 03:22:14

50

Views

The condition for the existence of a symmetric form for the reflection formula $f(1-x)= \chi (x) f(x)$

Published on 25 Mar 2026 - 3:22

score 573 · Answer 5 · 2019-04-13 10:17:57

573

Views

$2+ f(x)f(y)=f(x)+f(y) +f(xy) $, if $f(2)=5$ find $f(5)$

Published on 13 Apr 2019 - 10:17

score 129 · Answer 6 · 2019-04-17 14:56:33

129

Views

How to prove $f$ is $C^\infty$

Published on 17 Apr 2019 - 14:56

score 213 · Answer 7 · 2019-04-21 17:54:48

213

Views

Solve functional equation $f(z)=c+zf(z^2)$ with series expansion?

Published on 21 Apr 2019 - 17:54

score 66 · Answer 8 · 2019-04-22 15:49:43

66

Views

Find $x$ where $f(e^{(x+1)})=x-\ln(x)$ approaches one.

Published on 22 Apr 2019 - 15:49

score 103 · Answer 9 · 2019-04-23 09:31:47

103

Views

If $f(x)f(y)+f(xy)\le -\frac{1}{4},\forall x,y\in[0,1)$, show that $f(x)=-\frac{1}{2}$

Published on 23 Apr 2019 - 9:31

score 180 · Answer 10 · 2019-04-23 17:20:34

180

Views

Find all functions $f : \mathbb{(0,\infty})\to\mathbb{R}$ such that $f(x+y) = xf(y)+ yf(x)$

Published on 23 Apr 2019 - 17:20

score 73 · Answer 11 · 2019-04-24 07:04:12

$f: \mathbb{R} \to \mathbb{R},\space\space\space f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^2,\space\space$find $f(3)$ in terms of $f(0)$.

score 268 · Answer 12 · 2019-04-24 19:51:30

268

Views

Additive and Bijective function on the real line

Published on 24 Apr 2019 - 19:51

score 88 · Answer 13 · 2019-04-25 08:04:59

88

Views

Find all function $f:\ \Bbb{R}\ \longrightarrow\ \Bbb{R}$ such that : $f(ax)f(by)=f(ax+by)+cxy$ where $a,b,c>0$

Published on 25 Apr 2019 - 8:04

score 62 · Answer 14 · 2019-04-25 16:24:20

62

Views

Functions satisfying $f(2x)+f(3x)\leq k f(x)$

Published on 25 Apr 2019 - 16:24

score 190 · Answer 15 · 2019-04-25 23:24:46

190

Views

Power-like functional equation

Published on 25 Apr 2019 - 23:24

List Question

Multivariate polynomial functional equation

Find all real functions such that $(x + 1)f(xf(y)) = xf(y(x + 1))$

Find all functions $f$ for which $f(x-y) = f(x) + f(y) - 2xy$ for all real numbers $x$ and $y$.

The condition for the existence of a symmetric form for the reflection formula $f(1-x)= \chi (x) f(x)$

$2+ f(x)f(y)=f(x)+f(y) +f(xy) $, if $f(2)=5$ find $f(5)$

How to prove $f$ is $C^\infty$

Solve functional equation $f(z)=c+zf(z^2)$ with series expansion?

Find $x$ where $f(e^{(x+1)})=x-\ln(x)$ approaches one.

If $f(x)f(y)+f(xy)\le -\frac{1}{4},\forall x,y\in[0,1)$, show that $f(x)=-\frac{1}{2}$

Find all functions $f : \mathbb{(0,\infty})\to\mathbb{R}$ such that $f(x+y) = xf(y)+ yf(x)$

$f: \mathbb{R} \to \mathbb{R},\space\space\space f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^2,\space\space$find $f(3)$ in terms of $f(0)$.

Additive and Bijective function on the real line

Find all function $f:\ \Bbb{R}\ \longrightarrow\ \Bbb{R}$ such that : $f(ax)f(by)=f(ax+by)+cxy$ where $a,b,c>0$

Functions satisfying $f(2x)+f(3x)\leq k f(x)$

Power-like functional equation

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