List questions from functional-equations

194

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The functional equation $\big(1 + yf(x)\big)\big(1 - yf(x + y)\big) = 1$ for $f:\mathbb R^+\to\mathbb R^+$

Published on 26 Jun 2020 - 17:58

117

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Does there exist a number that makes this work?

Published on 28 Jun 2020 - 2:52

142

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Functional equation question involving fixed points

Published on 26 Mar 2026 - 4:50

306

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Find all polynomials satisfying $p(x)p(-x)=p(x^2)$

Published on 27 Mar 2026 - 21:05

845

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Find all functions which satisfy $f(m^2+n^2)=f(m)^2+f(n)^2$ $\forall\space m,n\in\Bbb{N}$ and $f(1)>0$

Published on 04 Jul 2020 - 6:46

125

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Local minimums of a functional in an interval

Published on 23 Feb 2026 - 12:04

433

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All solutions of $f(x)f(-x)=1$

Published on 06 Jul 2020 - 12:49

110

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Derivative of Functional Equations

Published on 08 Jul 2020 - 17:51

58

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Solving $f(x)$ in a functional equation

Published on 08 Jul 2020 - 19:20

157

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Continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f\big(f(x)\big)=rf(x)+sx$ and $r,s \in (0, 1/2).$

Published on 09 Jul 2020 - 0:03

89

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Are the only solutions to this implicit functional equation linear?

Published on 27 Mar 2026 - 15:05

48

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Is this solution unique?

Published on 09 Jul 2020 - 6:56

48

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Is $f(x) = mx + c$ the only set of solutions to $f(x + 1) - f(x) = \text{constant}$ where $m$, $c$, and $x$ are integers?

Published on 10 Jul 2020 - 19:37

52

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How can we Differentiate Cauchy's Formula for Repeated Integrals?

Published on 12 Jul 2020 - 8:16

232

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USAMO 2018 functional equation: $f(x +\frac{1}{y})+ f(y +\frac{1}{z})+ f(z + \frac{1}{x})= 1$ when $xyz=1$

Published on 12 Jul 2020 - 8:36

List Question

The functional equation $\big(1 + yf(x)\big)\big(1 - yf(x + y)\big) = 1$ for $f:\mathbb R^+\to\mathbb R^+$

Does there exist a number that makes this work?

Functional equation question involving fixed points

Find all polynomials satisfying $p(x)p(-x)=p(x^2)$

Find all functions which satisfy $f(m^2+n^2)=f(m)^2+f(n)^2$ $\forall\space m,n\in\Bbb{N}$ and $f(1)>0$

Local minimums of a functional in an interval

All solutions of $f(x)f(-x)=1$

Derivative of Functional Equations

Solving $f(x)$ in a functional equation

Continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f\big(f(x)\big)=rf(x)+sx$ and $r,s \in (0, 1/2).$

Are the only solutions to this implicit functional equation linear?

Is this solution unique?

Is $f(x) = mx + c$ the only set of solutions to $f(x + 1) - f(x) = \text{constant}$ where $m$, $c$, and $x$ are integers?

How can we Differentiate Cauchy's Formula for Repeated Integrals?

USAMO 2018 functional equation: $f(x +\frac{1}{y})+ f(y +\frac{1}{z})+ f(z + \frac{1}{x})= 1$ when $xyz=1$

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