List questions from functional-equations

Published on 15 Jun 2014 - 21:22

259

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A logarithm-like functional equation

Published on 16 Jun 2014 - 13:18

250

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A function satisfying $f(\frac1{x+1})\cdot x=f(x)-1$ and $f(1)=1$?

Published on 16 Jun 2014 - 14:20

92

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Higher Order Functional Equations

Published on 16 Jun 2014 - 21:59

277

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Real-analytic $f(z)=f\left(\sqrt z\right) + f\left(-\sqrt z\right)$?

Published on 25 Mar 2026 - 9:50

410

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Additive functional inequality

Published on 22 Jun 2014 - 21:50

556

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Functional equation and fixed points

Published on 23 Jun 2014 - 19:43

280

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Find $f$ such that $\frac{\mathrm d^2}{\mathrm dx^2}f(x)=f\left(\sqrt{x}\right)$.

Published on 23 Jun 2014 - 21:45

105

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Continuous functions such that $f(x)+f(x^2)=x$

Published on 25 Jun 2014 - 9:08

337

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functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$

Published on 01 Jul 2014 - 2:58

174

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General Solution of Functional Equation

Published on 02 Jul 2014 - 4:24

425

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find all functions $ f : \mathbb{R} \rightarrow \mathbb{R} $ such that : $ f(f(x))=x^2-2 $

Published on 02 Jul 2014 - 6:32

4.3k

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Find all the functions $f:\mathbb{R}→\mathbb{R}$ such that $f(mx+c)=mf(x)+c$

Published on 03 Jul 2014 - 5:22

533

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Solve functional equation $f(f(f(x)))+f(x)=2x$

Published on 04 Jul 2014 - 10:52

306

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Solving a second level functional equation over all functions $g$

Published on 25 Mar 2026 - 9:32

List Question

Understanding an Equation and how to implement it

A logarithm-like functional equation

A function satisfying $f(\frac1{x+1})\cdot x=f(x)-1$ and $f(1)=1$?

Higher Order Functional Equations

Real-analytic $f(z)=f\left(\sqrt z\right) + f\left(-\sqrt z\right)$?

Additive functional inequality

Functional equation and fixed points

Find $f$ such that $\frac{\mathrm d^2}{\mathrm dx^2}f(x)=f\left(\sqrt{x}\right)$.

Continuous functions such that $f(x)+f(x^2)=x$

functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$

General Solution of Functional Equation

find all functions $ f : \mathbb{R} \rightarrow \mathbb{R} $ such that : $ f(f(x))=x^2-2 $

Find all the functions $f:\mathbb{R}→\mathbb{R}$ such that $f(mx+c)=mf(x)+c$

Solve functional equation $f(f(f(x)))+f(x)=2x$

Solving a second level functional equation over all functions $g$

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