Question

Solution or property to a functional equation

score 161 · Answer 1 · 2024-02-28 13:52:11

161

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Solution or property to a functional equation

Published on 28 Feb 2024 - 13:52

score 70 · Answer 2 · 2024-02-28 22:52:20

70

Views

Solving equation involving shifts of the unknown function.

Published on 28 Feb 2024 - 22:52

score 97 · Answer 3 · 2024-03-01 13:00:57

97

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Find all continuous functions from $ ]0,+\infty[ \to ]0,+\infty[ $ that satisfy $\forall x\in ]0,+\infty[ , f(x) = f(x^a f(x)) $.

Published on 01 Mar 2024 - 13:00

score 108 · Answer 4 · 2024-03-01 20:19:57

108

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$f(x) + f(y) = f ( xy - 2024x - 2024y + 2024*2025 ) ,\forall x,y \in (2024,\infty)$

Published on 01 Mar 2024 - 20:19

score 108 · Answer 5 · 2026-03-27 12:27:56

108

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How do I solve this differential-integral equation?

Published on 27 Mar 2026 - 12:27

score 42 · Answer 6 · 2024-03-06 19:22:33

42

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Find all $f:\Bbb R\to\Bbb R$ st for any $x,y\in\mathbb R$, the multiset $\{(f(xf(y)+1),f(yf(x)-1)\}$ equals the multiset $\{xf(f(y))+1,yf(f(x))-1\}$.

Published on 06 Mar 2024 - 19:22

score 114 · Answer 7 · 2024-03-07 05:45:59

114

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How to solve $f(x)=\frac{1}{2} f(3x) + \cos x$?

Published on 07 Mar 2024 - 5:45

score 43 · Answer 8 · 2024-03-07 15:49:32

43

Views

$f(xf(y)+f(x))=yf(x)+x , \forall x,y \in \mathbb Q$

Published on 07 Mar 2024 - 15:49

score 44 · Answer 9 · 2024-03-08 00:15:55

44

Views

Trying to find a trig reduction relating sinc's and cos's.

Published on 08 Mar 2024 - 0:15

score 29 · Answer 10 · 2024-03-09 09:13:18

29

Views

Functional equation with certain properties

Published on 09 Mar 2024 - 9:13

score 78 · Answer 11 · 2024-03-09 17:26:01

78

Views

Can a non-constant function satisfy $f\left(\frac{x+y+1}{2}\right) = \frac{f(x)+f(y)}{2}$?

Published on 09 Mar 2024 - 17:26

score 394 · Answer 12 · 2024-03-09 17:49:32

394

Views

How to solve $y(y'(y''(\cdots(y^{(n)}(x))))) = f(x)$ for $y(x)$?

Published on 09 Mar 2024 - 17:49

score 16 · Answer 13 · 2026-02-23 21:10:04

16

Views

Function equation separability-like criterion

Published on 23 Feb 2026 - 21:10

score 254 · Answer 14 · 2024-03-15 16:04:18

254

Views

Does $f(x+f(y))=f(x)+f(y)$ imply $f(x+y)=f(x)+f(y)-f(0)$, given $f(0)\neq0$?

Published on 15 Mar 2024 - 16:04

score 44 · Answer 15 · 2024-03-16 09:44:41

44

Views

finding a function consisting of two variables

Published on 16 Mar 2024 - 9:44

List Question

Solution or property to a functional equation

Solving equation involving shifts of the unknown function.

Find all continuous functions from $ ]0,+\infty[ \to ]0,+\infty[ $ that satisfy $\forall x\in ]0,+\infty[ , f(x) = f(x^a f(x)) $.

$f(x) + f(y) = f ( xy - 2024x - 2024y + 2024*2025 ) ,\forall x,y \in (2024,\infty)$

How do I solve this differential-integral equation?

Find all $f:\Bbb R\to\Bbb R$ st for any $x,y\in\mathbb R$, the multiset $\{(f(xf(y)+1),f(yf(x)-1)\}$ equals the multiset $\{xf(f(y))+1,yf(f(x))-1\}$.

How to solve $f(x)=\frac{1}{2} f(3x) + \cos x$?

$f(xf(y)+f(x))=yf(x)+x , \forall x,y \in \mathbb Q$

Trying to find a trig reduction relating sinc's and cos's.

Functional equation with certain properties

Can a non-constant function satisfy $f\left(\frac{x+y+1}{2}\right) = \frac{f(x)+f(y)}{2}$?

How to solve $y(y'(y''(\cdots(y^{(n)}(x))))) = f(x)$ for $y(x)$?

Function equation separability-like criterion

Does $f(x+f(y))=f(x)+f(y)$ imply $f(x+y)=f(x)+f(y)-f(0)$, given $f(0)\neq0$?

finding a function consisting of two variables

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