Question

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

score 147 · Answer 1 · 2026-04-14 22:41:24

147

Views

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

Published on 14 Apr 2026 - 22:41

score 195 · Answer 2 · 2026-04-10 02:05:29

195

Views

Simple example of functional equation in Banach Algebra and how to solve it

Published on 10 Apr 2026 - 2:05

score 180 · Answer 3 · 2026-04-11 20:49:09

180

Views

Proof that Pearson correlation is/isn't a functional of the copula for a given pair of random variables

Published on 11 Apr 2026 - 20:49

score 107 · Answer 4 · 2026-04-16 18:58:09

107

Views

$f(x) = x f(\frac{1}{x})$ for $x>0$

Published on 16 Apr 2026 - 18:58

score 103 · Answer 5 · 2026-04-12 02:20:41

103

Views

D'Alembert functional equation without odditivity

Published on 12 Apr 2026 - 2:20

score 857 · Answer 6 · 2026-04-12 11:05:59

857

Views

Functional equation: $f(x)=xf(1/x)$

Published on 12 Apr 2026 - 11:05

score 142 · Answer 7 · 2026-04-08 18:36:58

142

Views

About the functional equation between $\zeta$ and $\Gamma$?

Published on 08 Apr 2026 - 18:36

score 123 · Answer 8 · 2026-04-15 20:17:24

Are there known solutions to this functional equation involving the square root? $A(x)=c\frac{A\left(\sqrt{x}\right)+A\left(-\sqrt{x}\right)}{2}+x^k$

score 75 · Answer 9 · 2026-04-16 12:18:26

75

Views

Finding all $ f: \mathbb{R} \to \mathbb{R}$ such that $ f(x+f(y))=f(x)+2xy^2+y^2f(y) $

Published on 16 Apr 2026 - 12:18

score 128 · Answer 10 · 2026-04-16 16:28:00

Finding all $f: \mathbb{R} \to \mathbb{R}$ such that $f\bigl(xf(y)+y\bigr)+f\bigl(-f(x)\bigr)=f\bigl(yf(x)-y\bigr)+y $

score 186 · Answer 11 · 2026-04-16 17:28:23

Finding all pairs of functions $f, g: \mathbb{R} \to \mathbb{R} $ which satisfy $f(x+y) = g\left(\frac{1}{x}+\frac{1}{y}\right)(xy)^{2008}$

score 200 · Answer 12 · 2026-04-15 22:40:19

200

Views

Finding $f:\mathbb R\to\mathbb R$ satisfying $f\bigl(yf(x+y)+f(x)\bigr)=4x+2yf(x+y)$

Published on 15 Apr 2026 - 22:40

score 80 · Answer 13 · 2026-04-17 06:30:32

80

Views

Finding all $f:\mathbb{R} \to \mathbb{R}$ such that $f(xf(x)+2y)=f(x^2)+f(y)+x+y-1$

Published on 17 Apr 2026 - 6:30

score 60 · Answer 14 · 2026-04-15 18:48:33

60

Views

Find all $f$ which satisfies $ f:\mathbb{R}_{\geq0} \rightarrow \mathbb{R}, f(x+y^2) \geq f(x)+y $

Published on 15 Apr 2026 - 18:48

score 75 · Answer 15 · 2026-04-15 15:45:13

75

Views

Find all $f$ which satisfies the condition: $f:\mathbb{R} \to \mathbb{R}, f(f(x+y)-f(x-y))=xy$

Published on 15 Apr 2026 - 15:45

List Question

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

Simple example of functional equation in Banach Algebra and how to solve it

Proof that Pearson correlation is/isn't a functional of the copula for a given pair of random variables

$f(x) = x f(\frac{1}{x})$ for $x>0$

D'Alembert functional equation without odditivity

Functional equation: $f(x)=xf(1/x)$

About the functional equation between $\zeta$ and $\Gamma$?

Are there known solutions to this functional equation involving the square root? $A(x)=c\frac{A\left(\sqrt{x}\right)+A\left(-\sqrt{x}\right)}{2}+x^k$

Finding all $ f: \mathbb{R} \to \mathbb{R}$ such that $ f(x+f(y))=f(x)+2xy^2+y^2f(y) $

Finding all $f: \mathbb{R} \to \mathbb{R}$ such that $f\bigl(xf(y)+y\bigr)+f\bigl(-f(x)\bigr)=f\bigl(yf(x)-y\bigr)+y $

Finding all pairs of functions $f, g: \mathbb{R} \to \mathbb{R} $ which satisfy $f(x+y) = g\left(\frac{1}{x}+\frac{1}{y}\right)(xy)^{2008}$

Finding $f:\mathbb R\to\mathbb R$ satisfying $f\bigl(yf(x+y)+f(x)\bigr)=4x+2yf(x+y)$

Finding all $f:\mathbb{R} \to \mathbb{R}$ such that $f(xf(x)+2y)=f(x^2)+f(y)+x+y-1$

Find all $f$ which satisfies $ f:\mathbb{R}_{\geq0} \rightarrow \mathbb{R}, f(x+y^2) \geq f(x)+y $

Find all $f$ which satisfies the condition: $f:\mathbb{R} \to \mathbb{R}, f(f(x+y)-f(x-y))=xy$

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