Question

Checking if the solution to the functional equation is correct $f(2x+f(y))=x+y+f(x)$

score 91 · Answer 1 · 2020-05-12 06:45:26

91

Views

Checking if the solution to the functional equation is correct $f(2x+f(y))=x+y+f(x)$

Published on 12 May 2020 - 6:45

score 88 · Answer 2 · 2026-03-27 02:36:08

88

Views

If $f(2x)=f(x)+f(2), \forall x > 1$ prove that $f$ in increasing

Published on 27 Mar 2026 - 2:36

score 91 · Answer 3 · 2026-03-25 18:49:39

91

Views

Functional inequality $f(x+y)f(x-y)\leq f^2(x)-f^2(y)$

Published on 25 Mar 2026 - 18:49

score 45 · Answer 4 · 2020-05-15 04:32:38

45

Views

Solving for a density function

Published on 15 May 2020 - 4:32

score 82 · Answer 5 · 2020-05-15 10:24:59

82

Views

Determining all $f : \mathbb R \to \mathbb R$ that satisfy $f\bigl(xf(y)\bigr) = x^{2002}f\bigl(f(y)\bigr)$

Published on 15 May 2020 - 10:24

score 50 · Answer 6 · 2020-05-16 21:32:49

50

Views

Periodic and odd function

Published on 16 May 2020 - 21:32

score 660 · Answer 7 · 2020-05-17 05:10:39

660

Views

Determining all $f : \mathbb R \to \mathbb R$ that satisfy $xf(x) - yf(y) = (x-y)f(x+y)$

Published on 17 May 2020 - 5:10

score 105 · Answer 8 · 2020-05-18 15:22:45

105

Views

Non continuous solutions to $f(\lambda x)=f(x)$

Published on 18 May 2020 - 15:22

score 298 · Answer 9 · 2020-05-19 05:36:58

298

Views

Find the maximum and minimum value of $f(x)$

Published on 19 May 2020 - 5:36

score 135 · Answer 10 · 2020-05-20 16:02:07

135

Views

Solving $f(x^2 + y) = f(x^{27} + 2y) + f(x^4)$

Published on 20 May 2020 - 16:02

score 46 · Answer 11 · 2020-05-20 17:00:36

46

Views

Does a functional equation $f : R → R$ include all solutions of $f : N → N$

Published on 20 May 2020 - 17:00

score 117 · Answer 12 · 2020-05-21 07:15:43

117

Views

Is operator $T^2=T$ with closed image and kernel bounded?

Published on 21 May 2020 - 7:15

score 256 · Answer 13 · 2020-05-22 04:04:09

256

Views

Help needed with the functional equation $f \big(x + y f (x)\big) = f (x) + xf (y)$

Published on 22 May 2020 - 4:04

score 51 · Answer 14 · 2020-05-22 06:46:04

51

Views

On wildness/existence of an arithmetic function.

Published on 22 May 2020 - 6:46

score 348 · Answer 15 · 2020-05-22 07:47:53

348

Views

Find all polynomials $P(x)$, so that $P[F(x)] = F[P(x)],P(0)=0$ where $F$ is a given function with the property $F(x)>x$ for all $x\ge0$

Published on 22 May 2020 - 7:47

List Question

Checking if the solution to the functional equation is correct $f(2x+f(y))=x+y+f(x)$

If $f(2x)=f(x)+f(2), \forall x > 1$ prove that $f$ in increasing

Functional inequality $f(x+y)f(x-y)\leq f^2(x)-f^2(y)$

Solving for a density function

Determining all $f : \mathbb R \to \mathbb R$ that satisfy $f\bigl(xf(y)\bigr) = x^{2002}f\bigl(f(y)\bigr)$

Periodic and odd function

Determining all $f : \mathbb R \to \mathbb R$ that satisfy $xf(x) - yf(y) = (x-y)f(x+y)$

Non continuous solutions to $f(\lambda x)=f(x)$

Find the maximum and minimum value of $f(x)$

Solving $f(x^2 + y) = f(x^{27} + 2y) + f(x^4)$

Does a functional equation $f : R → R$ include all solutions of $f : N → N$

Is operator $T^2=T$ with closed image and kernel bounded?

Help needed with the functional equation $f \big(x + y f (x)\big) = f (x) + xf (y)$

On wildness/existence of an arithmetic function.

Find all polynomials $P(x)$, so that $P[F(x)] = F[P(x)],P(0)=0$ where $F$ is a given function with the property $F(x)>x$ for all $x\ge0$

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