Question

$f(x^2) = xf(x)$ implies that $ f(x) = mx$?

score 5.3k · Answer 1 · 2012-02-15 01:01:35

5.3k

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$f(x^2) = xf(x)$ implies that $ f(x) = mx$?

Published on 15 Feb 2012 - 1:01

score 60 · Answer 2 · 2026-03-29 10:14:31

60

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In which cases iterative equations can be reduced to finite-difference equations?

Published on 29 Mar 2026 - 10:14

score 91 · Answer 3 · 2012-02-23 03:58:33

91

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Given that $f(x^2)=f(x)^2$ and $f(x+1)=f(x)+1$, try to find $f$

Published on 23 Feb 2012 - 3:58

score 1.4k · Answer 4 · 2026-03-31 08:06:07

1.4k

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3rd iterate of a continuous function equals identity function

Published on 31 Mar 2026 - 8:06

score 7.6k · Answer 5 · 2012-03-01 11:15:04

7.6k

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Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)

Published on 01 Mar 2012 - 11:15

score 1k · Answer 6 · 2026-03-29 10:09:38

1k

Views

Recurrence relations on a continuous domain

Published on 29 Mar 2026 - 10:09

score 187 · Answer 7 · 2012-03-16 06:53:46

187

Views

Find $f$ such that $\{f(x+y)\}=\{f(x)\}+\{f(y)\}$

Published on 16 Mar 2012 - 6:53

score 253 · Answer 8 · 2012-03-20 15:39:33

253

Views

Analytic solution of the functional equation $V\left(z^d\right)=dz^{d-1} V(z)+\sum_{k=2}^d b_k z^{d-k}$

Published on 20 Mar 2012 - 15:39

score 410 · Answer 9 · 2012-03-27 01:05:01

410

Views

What was this theorem called

Published on 27 Mar 2012 - 1:05

score 5.4k · Answer 10 · 2012-04-13 06:01:33

5.4k

Views

Graph of discontinuous additive function is dense in $ \mathbb R ^ 2 $

Published on 13 Apr 2012 - 6:01

score 277 · Answer 11 · 2012-04-13 09:21:53

277

Views

solution of d’Alembert’s equation: $g(x+y)+g(x-y)=2g(x)g(y)$

Published on 13 Apr 2012 - 9:21

score 470 · Answer 12 · 2012-04-13 12:23:44

470

Views

solve functional equation: $[f(x)]^2-[f(y)]^2$=$f(x+y)f(x-y)$

Published on 13 Apr 2012 - 12:23

score 6k · Answer 13 · 2012-04-14 04:13:00

6k

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I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.

Published on 14 Apr 2012 - 4:13

score 234 · Answer 14 · 2026-04-09 11:01:57

234

Views

Functional equation and Riemann function $ \xi(s) $

Published on 09 Apr 2026 - 11:01

score 104 · Answer 15 · 2012-05-01 02:25:48

104

Views

How to solve a functional equation of the form $1-g(f(s))=m(1-g(s))$?

Published on 01 May 2012 - 2:25

List Question

$f(x^2) = xf(x)$ implies that $ f(x) = mx$?

In which cases iterative equations can be reduced to finite-difference equations?

Given that $f(x^2)=f(x)^2$ and $f(x+1)=f(x)+1$, try to find $f$

3rd iterate of a continuous function equals identity function

Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)

Recurrence relations on a continuous domain

Find $f$ such that $\{f(x+y)\}=\{f(x)\}+\{f(y)\}$

Analytic solution of the functional equation $V\left(z^d\right)=dz^{d-1} V(z)+\sum_{k=2}^d b_k z^{d-k}$

What was this theorem called

Graph of discontinuous additive function is dense in $ \mathbb R ^ 2 $

solution of d’Alembert’s equation: $g(x+y)+g(x-y)=2g(x)g(y)$

solve functional equation: $[f(x)]^2-[f(y)]^2$=$f(x+y)f(x-y)$

I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.

Functional equation and Riemann function $ \xi(s) $

How to solve a functional equation of the form $1-g(f(s))=m(1-g(s))$?

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