List questions from functional-equations

Published on 09 Apr 2026 - 10:08

121

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How to find $f:\mathbb{Q}^+\to \mathbb{Q}^+$ if $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\bigl(f(x)\bigr)$

Published on 14 Mar 2013 - 1:10

2.8k

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

Published on 19 Mar 2013 - 20:00

104

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Properties of $g$ satisfying $f(x,x)[\nabla_{x}^{2}g(x,y)]_{x=y}+2[\nabla_{x}f(x,y)]_{x=y}\cdot[\nabla_{x}g(x,y)]_{x=y}=0$ for all $f$

Published on 19 Mar 2013 - 21:08

97

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Functional equation $m(x^y)=m(x)+m(y)$.

Published on 20 Mar 2013 - 7:14

778

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Polynomial: $p(x) = p(x+3)$.

Published on 24 Mar 2013 - 16:14

175

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Does a function exist with the property $f(-n^2+3n+1)=(f(n))^2+1$?

Published on 26 Mar 2013 - 7:07

156

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functional equations

Published on 26 Mar 2013 - 17:24

823

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More general reflection formula for Gamma function

Published on 10 Apr 2026 - 11:46

115

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"Foldable" functions

Published on 10 Apr 2026 - 14:25

217

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Generalization of Cauchy's functional equation

Published on 29 Mar 2013 - 13:06

105

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An odd function satisfying $g(1-t)+g(1+t)=-t$

Published on 30 Mar 2013 - 4:58

57

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Functional equation and whether the function is constant

Published on 09 Apr 2026 - 8:07

68

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$f : \mathbb{R} \to \mathbb{R}$, $f \in \mathscr{C}^{0}$. Find all $f \not \equiv 0$ satisfying a functional equation

Published on 01 Aug 2020 - 10:50

103

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How can I determinine all functions or a function f?

Published on 01 Aug 2020 - 14:57

List Question

How can prove this equation.

How to find $f:\mathbb{Q}^+\to \mathbb{Q}^+$ if $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\bigl(f(x)\bigr)$

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

Properties of $g$ satisfying $f(x,x)[\nabla_{x}^{2}g(x,y)]_{x=y}+2[\nabla_{x}f(x,y)]_{x=y}\cdot[\nabla_{x}g(x,y)]_{x=y}=0$ for all $f$

Functional equation $m(x^y)=m(x)+m(y)$.

Polynomial: $p(x) = p(x+3)$.

Does a function exist with the property $f(-n^2+3n+1)=(f(n))^2+1$?

functional equations

More general reflection formula for Gamma function

"Foldable" functions

Generalization of Cauchy's functional equation

An odd function satisfying $g(1-t)+g(1+t)=-t$

Functional equation and whether the function is constant

$f : \mathbb{R} \to \mathbb{R}$, $f \in \mathscr{C}^{0}$. Find all $f \not \equiv 0$ satisfying a functional equation

How can I determinine all functions or a function f?

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