Question

How to characterize homogenous functions?

score 56 · Answer 1 · 2026-04-10 19:41:40

How to characterize homogenous functions?

Published on 10 Apr 2026 - 19:41

score 77 · Answer 2 · 2026-04-15 22:28:06

Find $f(x)$ and $\lim_{x\to\infty} f(x)^x$ for $f'(0)=1$, $-1<f(x)<1$, and $f(x+y)=\frac{f(x)+f(y)}{1+f(x)f(y)}$ for all $x\in\mathbb{R}$

score 71 · Answer 3 · 2026-04-15 19:50:15

71

Views

An increasing function $f: \mathbb{N}_+\to \mathbb{R}$ s.t. $f(xy)=f(x)+f(y)$ for all $x,y\in \mathbb{N}_+$.

Published on 15 Apr 2026 - 19:50

score 163 · Answer 4 · 2026-04-09 11:53:27

163

Views

Integral functional equation

Published on 09 Apr 2026 - 11:53

score 64 · Answer 5 · 2026-04-14 19:28:13

64

Views

Solving a functional equation $ g(x) = \frac{1}{1-x} g\left(\frac{ax}{1-x}\right) $

Published on 14 Apr 2026 - 19:28

score 171 · Answer 6 · 2026-04-15 20:26:34

171

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Finding all functions satisfying $f(x f(x+y))+f(f(y) f(x+y))=(x+y)^{2}$

Published on 15 Apr 2026 - 20:26

score 134 · Answer 7 · 2026-04-16 18:05:32

134

Views

Smooth function satisfying $f^{-1}(x)=f(x+1/2)-1/2$

Published on 16 Apr 2026 - 18:05

score 17 · Answer 8 · 2026-04-14 02:59:17

17

Views

When do binary functions have non trivial meromorphic homomorphisms and why?

Published on 14 Apr 2026 - 2:59

score 211 · Answer 9 · 2026-04-11 01:05:22

211

Views

When does degree 1 polynomial commute?

Published on 11 Apr 2026 - 1:05

score 174 · Answer 10 · 2026-04-17 08:32:38

174

Views

When does linear polynomials commute over finte field?

Published on 17 Apr 2026 - 8:32

score 83 · Answer 11 · 2026-04-11 05:41:47

83

Views

The “hyperfabius” function

Published on 11 Apr 2026 - 5:41

score 94 · Answer 12 · 2026-04-14 21:29:16

94

Views

if $f(x)f(y) = y^h f(x/2) + x^k f(y/2)$ for all positive reals $x,y$, then $f$ must be identically zero

Published on 14 Apr 2026 - 21:29

score 66 · Answer 13 · 2026-04-17 05:31:03

66

Views

$f: \Bbb{R} \to \Bbb{R}, f(-y^2)+f(x^2+y)-y=(x+y)f(x-y).$

Published on 17 Apr 2026 - 5:31

score 73 · Answer 14 · 2026-04-10 21:55:36

73

Views

Functional equation with periods depending on $f$

Published on 10 Apr 2026 - 21:55

score 42 · Answer 15 · 2026-04-15 09:26:09

42

Views

Prove or disprove whether $h(x^q) = h(x)^q$ for all $x > 0$ and rational $q > 0$ and $h(x) = x^k$ for all $x > 0,$ where $k\ge 0.$

Published on 15 Apr 2026 - 9:26

List Question

How to characterize homogenous functions?

Find $f(x)$ and $\lim_{x\to\infty} f(x)^x$ for $f'(0)=1$, $-1<f(x)<1$, and $f(x+y)=\frac{f(x)+f(y)}{1+f(x)f(y)}$ for all $x\in\mathbb{R}$

An increasing function $f: \mathbb{N}_+\to \mathbb{R}$ s.t. $f(xy)=f(x)+f(y)$ for all $x,y\in \mathbb{N}_+$.

Integral functional equation

Solving a functional equation $ g(x) = \frac{1}{1-x} g\left(\frac{ax}{1-x}\right) $

Finding all functions satisfying $f(x f(x+y))+f(f(y) f(x+y))=(x+y)^{2}$

Smooth function satisfying $f^{-1}(x)=f(x+1/2)-1/2$

When do binary functions have non trivial meromorphic homomorphisms and why?

When does degree 1 polynomial commute?

When does linear polynomials commute over finte field?

The “hyperfabius” function

if $f(x)f(y) = y^h f(x/2) + x^k f(y/2)$ for all positive reals $x,y$, then $f$ must be identically zero

$f: \Bbb{R} \to \Bbb{R}, f(-y^2)+f(x^2+y)-y=(x+y)f(x-y).$

Functional equation with periods depending on $f$

Prove or disprove whether $h(x^q) = h(x)^q$ for all $x > 0$ and rational $q > 0$ and $h(x) = x^k$ for all $x > 0,$ where $k\ge 0.$

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