Question

Solving the functional equation $ xf(x) - yf(y) = (x - y)f(x + y) $

score 306 · Answer 1 · 2015-12-08 17:26:51

306

Views

Solving the functional equation $ xf(x) - yf(y) = (x - y)f(x + y) $

Published on 08 Dec 2015 - 17:26

score 230 · Answer 2 · 2015-12-09 13:37:11

230

Views

discontinuous solutions of the functional equation $f\left(a^b\right) = f(a)^{f(b)}$

Published on 09 Dec 2015 - 13:37

score 4.8k · Answer 3 · 2015-12-09 15:29:14

4.8k

Views

Functional equation $f(xy)=f(x)+f(y)$ and continuity

Published on 09 Dec 2015 - 15:29

score 3.1k · Answer 4 · 2015-12-09 20:13:23

3.1k

Views

Find all functions $f$ such that $f(x-f(y)) = f(f(x)) - f(y) - 1$

Published on 09 Dec 2015 - 20:13

score 72 · Answer 5 · 2026-03-27 15:36:20

72

Views

How can one show that $f(n)>n$

Published on 27 Mar 2026 - 15:36

score 227 · Answer 6 · 2015-12-10 17:52:33

227

Views

The functional equation $f(f(x)+xf(y))=xf(y+1)$

Published on 10 Dec 2015 - 17:52

score 1.2k · Answer 7 · 2015-12-11 15:39:15

1.2k

Views

d'Alembert functional equation: $f(x+y)+f(x-y)=2f(x)f(y)$

Published on 11 Dec 2015 - 15:39

score 387 · Answer 8 · 2015-12-13 16:07:41

387

Views

The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $

Published on 13 Dec 2015 - 16:07

score 259 · Answer 9 · 2015-12-14 00:29:33

259

Views

Do I need to verify solutions to functional equations?

Published on 14 Dec 2015 - 0:29

score 204 · Answer 10 · 2015-12-14 02:21:50

204

Views

Finding a unique continuous $g$ on $[0,1]$ satisfying $g(x) = \frac{1}{2}g\left(\frac{x+1}{2}\right) + f(x)$ for given $f$

Published on 14 Dec 2015 - 2:21

score 83 · Answer 11 · 2015-12-15 00:41:20

83

Views

Verify proof of $ f(x)=e^x $ if $ f(x+y)=f(x)f(y) $ and $ f'(x)$ exists for all $x$

Published on 15 Dec 2015 - 0:41

score 104 · Answer 12 · 2015-12-15 19:25:13

104

Views

$3^x-2^y=1$, $x \in \mathbb{N}$ and $y \in \mathbb{N}$

Published on 15 Dec 2015 - 19:25

score 151 · Answer 13 · 2015-12-15 23:12:19

151

Views

How can one show that $f(0)=0$ for $f$ satisfying certain conditions?

Published on 15 Dec 2015 - 23:12

score 162 · Answer 14 · 2015-12-16 12:25:42

162

Views

About $f(x)= f(\frac{1}{x})$

Published on 16 Dec 2015 - 12:25

score 92 · Answer 15 · 2015-12-16 13:02:07

92

Views

Let $f:\mathbb{R}^m \to \mathbb{R}$ be differentiable s.t. $f(x/2)=f(x)/2, \forall x \in \mathbb{R}^m$. Show that $f$ is linear.

Published on 16 Dec 2015 - 13:02

List Question

Solving the functional equation $ xf(x) - yf(y) = (x - y)f(x + y) $

discontinuous solutions of the functional equation $f\left(a^b\right) = f(a)^{f(b)}$

Functional equation $f(xy)=f(x)+f(y)$ and continuity

Find all functions $f$ such that $f(x-f(y)) = f(f(x)) - f(y) - 1$

How can one show that $f(n)>n$

The functional equation $f(f(x)+xf(y))=xf(y+1)$

d'Alembert functional equation: $f(x+y)+f(x-y)=2f(x)f(y)$

The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $

Do I need to verify solutions to functional equations?

Finding a unique continuous $g$ on $[0,1]$ satisfying $g(x) = \frac{1}{2}g\left(\frac{x+1}{2}\right) + f(x)$ for given $f$

Verify proof of $ f(x)=e^x $ if $ f(x+y)=f(x)f(y) $ and $ f'(x)$ exists for all $x$

$3^x-2^y=1$, $x \in \mathbb{N}$ and $y \in \mathbb{N}$

How can one show that $f(0)=0$ for $f$ satisfying certain conditions?

About $f(x)= f(\frac{1}{x})$

Let $f:\mathbb{R}^m \to \mathbb{R}$ be differentiable s.t. $f(x/2)=f(x)/2, \forall x \in \mathbb{R}^m$. Show that $f$ is linear.

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