Question

About solving $f(z) = \frac{1}{4} (f(-1-z) +2 f(-1-2z)+ 2f(-1+2z) +f(-1+z))$

score 185 · Answer 1 · 2019-11-12 05:46:11

185

Views

About solving $f(z) = \frac{1}{4} (f(-1-z) +2 f(-1-2z)+ 2f(-1+2z) +f(-1+z))$

Published on 12 Nov 2019 - 5:46

score 42 · Answer 2 · 2019-11-12 06:08:50

42

Views

the solution of a functional equation

Published on 12 Nov 2019 - 6:08

score 41 · Answer 3 · 2019-11-12 19:07:49

41

Views

'Inverse' type transform of a given functional equation

Published on 12 Nov 2019 - 19:07

score 57 · Answer 4 · 2019-11-12 20:03:30

57

Views

Closed form for functional equation $g(x)=\frac{1}{2}(g(x^2)+g((1-x)^2))$ on $[0,1]$

Published on 12 Nov 2019 - 20:03

score 1.3k · Answer 5 · 2019-11-14 16:05:35

1.3k

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Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $

Published on 14 Nov 2019 - 16:05

score 121 · Answer 6 · 2026-03-27 21:17:56

121

Views

Looking for more properties & references for what I call backward harmonic functions

Published on 27 Mar 2026 - 21:17

score 175 · Answer 7 · 2019-11-16 14:20:40

175

Views

Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.

Published on 16 Nov 2019 - 14:20

score 498 · Answer 8 · 2026-03-25 22:26:50

498

Views

Find all functions $f$ such that $f:\mathbb{R}\rightarrow \mathbb{R}$ and $f\big(f(x)-x+y^2\big)=yf(y)$.

Published on 25 Mar 2026 - 22:26

score 95 · Answer 9 · 2019-11-17 15:29:45

95

Views

Minimizing an action that leads to a non-linear second order differential equation of the Emden-Fowler type

Published on 17 Nov 2019 - 15:29

score 50 · Answer 10 · 2019-11-19 15:54:15

50

Views

Functional Equation $\frac{g(x)}{g(-x)} = r^{2x}$

Published on 19 Nov 2019 - 15:54

score 155 · Answer 11 · 2019-11-20 11:58:35

155

Views

Prove that f(2000x)=2000f(x)

Published on 20 Nov 2019 - 11:58

score 51 · Answer 12 · 2019-11-23 21:07:12

51

Views

$f(x_1)=g(x_2)$ for any $x=(x_1,x_2)$; then $f$ and $g$ are constant functions

Published on 23 Nov 2019 - 21:07

score 42 · Answer 13 · 2019-11-24 15:10:50

42

Views

Find real solutions for p(b)

Published on 24 Nov 2019 - 15:10

score 339 · Answer 14 · 2019-11-25 11:10:39

339

Views

A function that verifies the property $f(ab) = f(a) + f(b)$

Published on 25 Nov 2019 - 11:10

score 112 · Answer 15 · 2019-11-25 17:42:45

112

Views

A compounded integer functional equation $f \big(f^2(m) + 2f^2(n)\big) = m^2 + 2 n^2$

Published on 25 Nov 2019 - 17:42

List Question

About solving $f(z) = \frac{1}{4} (f(-1-z) +2 f(-1-2z)+ 2f(-1+2z) +f(-1+z))$

the solution of a functional equation

'Inverse' type transform of a given functional equation

Closed form for functional equation $g(x)=\frac{1}{2}(g(x^2)+g((1-x)^2))$ on $[0,1]$

Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $

Looking for more properties & references for what I call backward harmonic functions

Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.

Find all functions $f$ such that $f:\mathbb{R}\rightarrow \mathbb{R}$ and $f\big(f(x)-x+y^2\big)=yf(y)$.

Minimizing an action that leads to a non-linear second order differential equation of the Emden-Fowler type

Functional Equation $\frac{g(x)}{g(-x)} = r^{2x}$

Prove that f(2000x)=2000f(x)

$f(x_1)=g(x_2)$ for any $x=(x_1,x_2)$; then $f$ and $g$ are constant functions

Find real solutions for p(b)

A function that verifies the property $f(ab) = f(a) + f(b)$

A compounded integer functional equation $f \big(f^2(m) + 2f^2(n)\big) = m^2 + 2 n^2$

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