List questions from functional-equations

Published on 02 Sep 2017 - 4:03

143

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Sequence : $f(f(n))+f(n+1)=3n$

Published on 02 Sep 2017 - 12:15

120

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$f:[0,1]\rightarrow [0,1]$ and $f\circ f$ are not identically zero but $f(f(f(x)))=0$ for all $x\in [0,1]$. Does $f$ exist?

Published on 03 Sep 2017 - 9:47

22

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A weak version of Cauchy's inequality on a finite set of integers

Published on 04 Sep 2017 - 21:13

90

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A differential functional equation with quotient

Published on 05 Sep 2017 - 6:20

710

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Solutions to $(x+y)f(x+y)=xf(x)+yf(y)$

Published on 06 Sep 2017 - 0:57

1.4k

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Functional square root of $f(x)=x^2-1$???

Published on 30 Mar 2026 - 14:40

84

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Functional equation : $f[X-f[X]]=f[X]-f[f[X]]$

Published on 09 Sep 2017 - 9:47

390

Views

A question about specific function with this property $f(x+y)=f(x)f(y)$

Published on 11 Sep 2017 - 18:56

96

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Could one define a function in the following way, without leading to a contradiction?

Published on 13 Sep 2017 - 10:04

85

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Additive Cauchy functional equation with quotient of functions $\frac{f(x+y)}{g(x+y)} + B = \frac{f(x)}{g(x)} + \frac{f(y)}{g(y)} $

Published on 14 Sep 2017 - 10:24

175

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Functional equation : $ f(f(x))=bxf(x)+a$

Published on 16 Sep 2017 - 5:56

1.1k

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Prove $f(x)$ is quadratic if $f(2x)=4f(x)$ and $f(x)$ is increasing over positive $x$

Published on 16 Sep 2017 - 7:21

136

Views

Eigenfunctions of a Linear Operator

Published on 28 Mar 2026 - 2:21

161

Views

Closed Form for $\sum_{n=0}^{\infty}x^{2^n}$

Published on 17 Sep 2017 - 2:08

List Question

There does not exist $f(f(x))=x^2-2016$

Sequence : $f(f(n))+f(n+1)=3n$

$f:[0,1]\rightarrow [0,1]$ and $f\circ f$ are not identically zero but $f(f(f(x)))=0$ for all $x\in [0,1]$. Does $f$ exist?

A weak version of Cauchy's inequality on a finite set of integers

A differential functional equation with quotient

Solutions to $(x+y)f(x+y)=xf(x)+yf(y)$

Functional square root of $f(x)=x^2-1$???

Functional equation : $f[X-f[X]]=f[X]-f[f[X]]$

A question about specific function with this property $f(x+y)=f(x)f(y)$

Could one define a function in the following way, without leading to a contradiction?

Additive Cauchy functional equation with quotient of functions $\frac{f(x+y)}{g(x+y)} + B = \frac{f(x)}{g(x)} + \frac{f(y)}{g(y)} $

Functional equation : $ f(f(x))=bxf(x)+a$

Prove $f(x)$ is quadratic if $f(2x)=4f(x)$ and $f(x)$ is increasing over positive $x$

Eigenfunctions of a Linear Operator

Closed Form for $\sum_{n=0}^{\infty}x^{2^n}$

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