Question

Functional equation $ f ( x + y ) f ( x - y ) = f ^ 2 ( x ) $

score 79 · Answer 1 · 2019-02-08 08:43:04

79

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Functional equation $ f ( x + y ) f ( x - y ) = f ^ 2 ( x ) $

Published on 08 Feb 2019 - 8:43

score 140 · Answer 2 · 2026-03-25 07:47:11

140

Views

A Golden Ratio Functional Equation Sequence

Published on 25 Mar 2026 - 7:47

score 73 · Answer 3 · 2019-02-08 20:14:25

73

Views

Find $f(x)$ where $f(x)(A-\frac{B}{x+B/A})+Cf(x+\frac{B}{A})=0$.

Published on 08 Feb 2019 - 20:14

score 76 · Answer 4 · 2019-02-08 21:59:51

76

Views

Jensen like: $f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2} $for $x,y \in \mathbb{R}$ that $x-y \in \mathbb{Z}$

Published on 08 Feb 2019 - 21:59

score 148 · Answer 5 · 2019-02-09 00:40:49

148

Views

Functional equation $ (n+1) f(n+1)= (a n+b) f(n) $ for $n=0,1,...$

Published on 09 Feb 2019 - 0:40

score 39 · Answer 6 · 2019-02-10 06:46:43

39

Views

Smallest set of reals $\{r_{i}\}$ that ensures an additive function $f$ is linear if $f(r_{i})=f(1)r_{i}$ for all $r_{i}$

Published on 10 Feb 2019 - 6:46

score 179 · Answer 7 · 2019-02-14 23:12:24

179

Views

Determine all the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that, for every $x \in \mathbb{R}$, $f(2x) = 2f(x)$ .

Published on 14 Feb 2019 - 23:12

score 55 · Answer 8 · 2026-03-25 23:15:56

55

Views

How to construct a function with these hypotheses?

Published on 25 Mar 2026 - 23:15

score 939 · Answer 9 · 2019-02-17 15:10:31

939

Views

How many polynomial functions exist such that $f(x^2) = (f(x))^2 = f(f(x))$

Published on 17 Feb 2019 - 15:10

score 101 · Answer 10 · 2026-03-01 02:34:36

101

Views

Formal group law and Koenigs function conjecture !?

Published on 01 Mar 2026 - 2:34

score 80 · Answer 11 · 2019-02-24 12:49:11

80

Views

A function describes $g(x + y) = g(x)g(y)$ for all $x, y$. If $g(4) = + 3,$ find the value of $g(–8)$?

Published on 24 Feb 2019 - 12:49

score 67 · Answer 12 · 2019-02-25 15:42:19

67

Views

Existence and uniqueness of a solution of a sort of ODE

Published on 25 Feb 2019 - 15:42

score 438 · Answer 13 · 2019-02-26 12:37:54

438

Views

How can I find y?

Published on 26 Feb 2019 - 12:37

score 407 · Answer 14 · 2019-03-01 02:01:02

Determining all functions satisfying the functional equation $ f \big( x + y f ( x ) \big) + f ( x y ) = f ( x ) + f ( 2019 y ) $

score 232 · Answer 15 · 2019-03-01 06:43:14

232

Views

Find $f$ such that $f(a-b)+f(c-d)=f(a)+f(b+c)+f(d)$

Published on 01 Mar 2019 - 6:43

List Question

Functional equation $ f ( x + y ) f ( x - y ) = f ^ 2 ( x ) $

A Golden Ratio Functional Equation Sequence

Find $f(x)$ where $f(x)(A-\frac{B}{x+B/A})+Cf(x+\frac{B}{A})=0$.

Jensen like: $f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2} $for $x,y \in \mathbb{R}$ that $x-y \in \mathbb{Z}$

Functional equation $ (n+1) f(n+1)= (a n+b) f(n) $ for $n=0,1,...$

Smallest set of reals $\{r_{i}\}$ that ensures an additive function $f$ is linear if $f(r_{i})=f(1)r_{i}$ for all $r_{i}$

Determine all the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that, for every $x \in \mathbb{R}$, $f(2x) = 2f(x)$ .

How to construct a function with these hypotheses?

How many polynomial functions exist such that $f(x^2) = (f(x))^2 = f(f(x))$

Formal group law and Koenigs function conjecture !?

A function describes $g(x + y) = g(x)g(y)$ for all $x, y$. If $g(4) = + 3,$ find the value of $g(–8)$?

Existence and uniqueness of a solution of a sort of ODE

How can I find y?

Determining all functions satisfying the functional equation $ f \big( x + y f ( x ) \big) + f ( x y ) = f ( x ) + f ( 2019 y ) $

Find $f$ such that $f(a-b)+f(c-d)=f(a)+f(b+c)+f(d)$

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