Question

Existence of $f(x)$

score 75 · Answer 1 · 2019-05-11 18:54:57

75

Views

Existence of $f(x)$

Published on 11 May 2019 - 18:54

score 44 · Answer 2 · 2019-05-13 11:43:17

44

Views

Suppose $L$ has a regular parametrix . Assume $U$ is a distribution given in an open set $\Omega \subset R^d$ and $L(U)=f$ , then $U$ is $C^{\infty}$

Published on 13 May 2019 - 11:43

score 336 · Answer 3 · 2019-05-13 15:43:35

336

Views

$2f(x)=f(y) \Rightarrow 2f(tx)=f(ty)$

Published on 13 May 2019 - 15:43

score 1.3k · Answer 4 · 2019-05-15 13:28:34

1.3k

Views

Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$

Published on 15 May 2019 - 13:28

score 311 · Answer 5 · 2019-05-16 14:51:13

311

Views

About the linear functional equations: $f(x+a) = bf(x)$ and $f(ax) = bf(x)$.

Published on 16 May 2019 - 14:51

score 214 · Answer 6 · 2019-05-17 17:27:23

214

Views

Prove that $\forall x \in \mathbb{R}, f(x)=0$

Published on 17 May 2019 - 17:27

score 22 · Answer 7 · 2026-03-25 06:10:38

22

Views

How to extract associative binary operations from a class of binary operations on $\mathbb{R}$

Published on 25 Mar 2026 - 6:10

score 219 · Answer 8 · 2019-05-19 15:35:46

219

Views

Solution of the equation $f(ax) = bf(x)$

Published on 19 May 2019 - 15:35

score 365 · Answer 9 · 2019-05-19 17:14:03

365

Views

Does there exist a function $f_{\Box,\Box}(\Box)$ making the formula $a + (b \oplus c) = (f_{b,c}(a)+b) \oplus (f_{c,b}(a)+c)$ true?

Published on 19 May 2019 - 17:14

score 69 · Answer 10 · 2019-05-20 05:57:35

69

Views

A problem on number of solutions of a functional equation: $ f ( x ) = 8 f ( 2 x + 1 ) $

Published on 20 May 2019 - 5:57

score 117 · Answer 11 · 2019-05-21 14:41:47

Differential Equation with inverse function $\frac{1-f^{-1}\left(\frac{f(x)}{x}\right)}{1-x} = 1- \frac{f(x)}{xf'(x)}$

score 181 · Answer 12 · 2019-05-29 17:32:28

181

Views

Find all function $f$ : $f(x+y)=e^{2xy}f(x)f(y)$

Published on 29 May 2019 - 17:32

score 418 · Answer 13 · 2019-05-29 19:35:31

418

Views

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

Published on 29 May 2019 - 19:35

score 273 · Answer 14 · 2019-05-30 03:05:06

273

Views

Complicated rational number functional equation: $f \left( x + \frac{y}{x} \right) = f(x) + \frac{f(y)}{f(x)} + 2y$

Published on 30 May 2019 - 3:05

score 1.7k · Answer 15 · 2026-03-25 18:56:32

1.7k

Views

$f(ax)=f(x)^2-1$, what is $f$?

Published on 25 Mar 2026 - 18:56

List Question

Existence of $f(x)$

Suppose $L$ has a regular parametrix . Assume $U$ is a distribution given in an open set $\Omega \subset R^d$ and $L(U)=f$ , then $U$ is $C^{\infty}$

$2f(x)=f(y) \Rightarrow 2f(tx)=f(ty)$

Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$

About the linear functional equations: $f(x+a) = bf(x)$ and $f(ax) = bf(x)$.

Prove that $\forall x \in \mathbb{R}, f(x)=0$

How to extract associative binary operations from a class of binary operations on $\mathbb{R}$

Solution of the equation $f(ax) = bf(x)$

Does there exist a function $f_{\Box,\Box}(\Box)$ making the formula $a + (b \oplus c) = (f_{b,c}(a)+b) \oplus (f_{c,b}(a)+c)$ true?

A problem on number of solutions of a functional equation: $ f ( x ) = 8 f ( 2 x + 1 ) $

Differential Equation with inverse function $\frac{1-f^{-1}\left(\frac{f(x)}{x}\right)}{1-x} = 1- \frac{f(x)}{xf'(x)}$

Find all function $f$ : $f(x+y)=e^{2xy}f(x)f(y)$

Which positive continuous functions satisfy $F(x) = F(e^x)-F(e^{-x})$ for $x\geq 0$?

Complicated rational number functional equation: $f \left( x + \frac{y}{x} \right) = f(x) + \frac{f(y)}{f(x)} + 2y$

$f(ax)=f(x)^2-1$, what is $f$?

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