Question

Differential functional equation

score 68 · Answer 1 · 2018-09-04 07:15:29

68

Views

Differential functional equation

Published on 04 Sep 2018 - 7:15

score 367 · Answer 2 · 2018-09-04 17:14:52

367

Views

Maximisation of a functional under integral constraint

Published on 04 Sep 2018 - 17:14

score 93 · Answer 3 · 2026-03-25 09:28:14

93

Views

Are constant and identity only analytic functions such that $f(f(x))=f(x)$?

Published on 25 Mar 2026 - 9:28

score 111 · Answer 4 · 2018-09-11 20:15:16

111

Views

determining every function $f$ defined for positive numbers satisfying $f\big(xf(y)\big)f(y)=f(x+y)$, $f(2)=0$ and $f(x)\ne 0$ for $0\le x<2$

Published on 11 Sep 2018 - 20:15

score 130 · Answer 5 · 2018-09-14 13:20:42

130

Views

Functions satisfying $f(x)+f(\frac{1}{1-x})=x$ with $x\in\mathbb{R}\setminus\{0,1\}.$

Published on 14 Sep 2018 - 13:20

score 120 · Answer 6 · 2018-09-15 06:59:54

120

Views

Find all non-negative integer $n$ that satisfy $f(x+1)+f(x-1)=\sqrt nf(x)$

Published on 15 Sep 2018 - 6:59

score 70 · Answer 7 · 2026-03-25 07:44:56

70

Views

Functional equation $f(a)·f(b)=\Bigl\lbrace\frac{1}{ab}\Bigr\rbrace$

Published on 25 Mar 2026 - 7:44

score 113 · Answer 8 · 2018-09-17 00:53:45

113

Views

If $f(f(x))=-f(x)$,does it necessarily follow that $f(x)=-x$?

Published on 17 Sep 2018 - 0:53

score 192 · Answer 9 · 2018-09-20 01:08:08

192

Views

How to solve equations in the form $af^2(x)+bf(x)+cx=0$?

Published on 20 Sep 2018 - 1:08

score 405 · Answer 10 · 2018-09-21 21:54:43

405

Views

Functions satisfying $f(x+y)+f(x-y)=2f(x)g(y)$

Published on 21 Sep 2018 - 21:54

score 175 · Answer 11 · 2018-09-22 11:37:20

175

Views

Are there any real-valued functions, besides logarithms, for which $f(x*y) = f(x) + f(y)$?

Published on 22 Sep 2018 - 11:37

score 346 · Answer 12 · 2018-09-23 20:51:15

346

Views

A functional equation of a matrix

Published on 23 Sep 2018 - 20:51

score 209 · Answer 13 · 2018-09-25 05:18:13

209

Views

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

Published on 25 Sep 2018 - 5:18

score 68 · Answer 14 · 2018-09-26 08:38:14

68

Views

Proving the function with this property is bijective

Published on 26 Sep 2018 - 8:38

score 513 · Answer 15 · 2018-09-26 15:20:00

513

Views

Finding $f(9999)$ if $f(1) = 2$ and $f(mn) = f(m) \, f(n) - f(m+n) + 1001$ for $m$ or $n$ equal to $1$

Published on 26 Sep 2018 - 15:20

List Question

Differential functional equation

Maximisation of a functional under integral constraint

Are constant and identity only analytic functions such that $f(f(x))=f(x)$?

determining every function $f$ defined for positive numbers satisfying $f\big(xf(y)\big)f(y)=f(x+y)$, $f(2)=0$ and $f(x)\ne 0$ for $0\le x<2$

Functions satisfying $f(x)+f(\frac{1}{1-x})=x$ with $x\in\mathbb{R}\setminus\{0,1\}.$

Find all non-negative integer $n$ that satisfy $f(x+1)+f(x-1)=\sqrt nf(x)$

Functional equation $f(a)·f(b)=\Bigl\lbrace\frac{1}{ab}\Bigr\rbrace$

If $f(f(x))=-f(x)$,does it necessarily follow that $f(x)=-x$?

How to solve equations in the form $af^2(x)+bf(x)+cx=0$?

Functions satisfying $f(x+y)+f(x-y)=2f(x)g(y)$

Are there any real-valued functions, besides logarithms, for which $f(x*y) = f(x) + f(y)$?

A functional equation of a matrix

Find all functions $f:\mathbb{N}^+\to\mathbb{N}^+$ such that $f\big(f(n)\big)+f(n)=2n$ for every $n\in\mathbb{N}^+$.

Proving the function with this property is bijective

Finding $f(9999)$ if $f(1) = 2$ and $f(mn) = f(m) \, f(n) - f(m+n) + 1001$ for $m$ or $n$ equal to $1$

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