Question

A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere

score 786 · Answer 1 · 2012-05-05 07:39:44

786

Views

A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere

Published on 05 May 2012 - 7:39

score 2.9k · Answer 2 · 2012-05-05 08:20:47

2.9k

Views

continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$

Published on 05 May 2012 - 8:20

score 536 · Answer 3 · 2012-05-07 14:49:21

536

Views

Functional equation $g(x+y) = g(x)g(y)$

Published on 07 May 2012 - 14:49

score 1.9k · Answer 4 · 2026-04-10 13:37:24

1.9k

Views

Riemann's thinking on symmetrizing the zeta functional equation

Published on 10 Apr 2026 - 13:37

score 8.6k · Answer 5 · 2012-05-13 12:02:04

8.6k

Views

If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$

Published on 13 May 2012 - 12:02

score 1.3k · Answer 6 · 2012-05-21 06:19:08

1.3k

Views

Solving a discrete functional equation: $a_1=0$, $a_{p+1}=n$ and $\sum_{i=a_{k+1}}^{a_{k+2}}n-(i+1)=\sum_{i=a_k}^{a_{k+1}}n-(i+1)$

Published on 21 May 2012 - 6:19

score 6.6k · Answer 7 · 2012-05-29 04:19:59

6.6k

Views

If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere

Published on 29 May 2012 - 4:19

score 1.3k · Answer 8 · 2012-05-31 18:05:02

1.3k

Views

$f(m + f(n)) = f(f(m)) + f(n)$

Published on 31 May 2012 - 18:05

score 7.4k · Answer 9 · 2012-06-01 21:05:12

7.4k

Views

Continuous and additive implies linear

Published on 01 Jun 2012 - 21:05

score 1.1k · Answer 10 · 2012-06-02 16:47:46

1.1k

Views

What can we say about functions satisfying $f(a + b) = f(a)f(b) $ for all $a,b\in \mathbb{R}$?

Published on 02 Jun 2012 - 16:47

score 546 · Answer 11 · 2012-06-05 15:33:37

Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$

score 2k · Answer 12 · 2012-06-14 05:02:21

2k

Views

Find all functions with $f(x + y) + f(x - y) = 2 f(x) f(y)$ and $\lim\limits_{x\to\infty}f(x)=0$.

Published on 14 Jun 2012 - 5:02

score 1k · Answer 13 · 2026-04-09 23:09:28

1k

Views

Equation about generating functions and subfactorial

Published on 09 Apr 2026 - 23:09

score 297 · Answer 14 · 2012-06-25 07:22:51

297

Views

Solve functional equation $f(x_1 x_2) = g_1(x_1) g_2(x_2)$

Published on 25 Jun 2012 - 7:22

score 69 · Answer 15 · 2012-06-26 17:55:14

69

Views

if I get the asymptotic solution of a certain equation involving $ f(x)$ does it mean that the solution exists

Published on 26 Jun 2012 - 17:55

List Question

A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere

continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$

Functional equation $g(x+y) = g(x)g(y)$

Riemann's thinking on symmetrizing the zeta functional equation

If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$

Solving a discrete functional equation: $a_1=0$, $a_{p+1}=n$ and $\sum_{i=a_{k+1}}^{a_{k+2}}n-(i+1)=\sum_{i=a_k}^{a_{k+1}}n-(i+1)$

If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere

$f(m + f(n)) = f(f(m)) + f(n)$

Continuous and additive implies linear

What can we say about functions satisfying $f(a + b) = f(a)f(b) $ for all $a,b\in \mathbb{R}$?

Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$

Find all functions with $f(x + y) + f(x - y) = 2 f(x) f(y)$ and $\lim\limits_{x\to\infty}f(x)=0$.

Equation about generating functions and subfactorial

Solve functional equation $f(x_1 x_2) = g_1(x_1) g_2(x_2)$

if I get the asymptotic solution of a certain equation involving $ f(x)$ does it mean that the solution exists

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