List questions from functional-equations

Published on 27 Mar 2020 - 18:42

55

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Polynomial equation involving $\cos(x)$

Published on 28 Mar 2020 - 17:49

125

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Functional Equation $f(xf(y) + f(x)) + f(y^2) = f(x) + y(f(x+y))$

Published on 29 Mar 2020 - 23:10

174

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IMO 1994 problem 5

Published on 26 Mar 2026 - 22:50

55

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Solution of the functional equation $f(x)f(y)=f(x+y)+xy$

Published on 30 Mar 2020 - 14:28

114

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How to solve the equation $a(f(x))^2 - af(kx)f(x) + xf’(x) = 0$

Published on 30 Mar 2020 - 14:42

734

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Functional equation $ f(x) + f\left(1-\frac{1}{x}\right) = \tan^{-1}(x) $ and definite integral

Published on 31 Mar 2020 - 9:57

83

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Find all functions $f$ such that $f(f(x)+yz)=x+f(y)f(z)$

Published on 31 Mar 2020 - 14:18

107

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IMO $2011$ problem $3$, how can I prove that $f(x) = 0, \; \forall \; x \leq 0 $?

Published on 31 Mar 2020 - 18:32

166

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Solving Olympiad Functional equations: $f(xy)=f(x)f(y)$ and $f(x+z)=f(x)+f(z)$ for some $z\ne0$

Published on 01 Apr 2020 - 6:04

41

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Linear equation with two unknowns

Published on 01 Apr 2020 - 7:50

283

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Olympiad Functional Equation $f(xf(y))=yf(x)$

Published on 01 Apr 2020 - 12:08

64

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Necessary and sufficient condition for a function to be contraction

Published on 01 Apr 2020 - 15:24

156

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Find all $f$ such that $f(x+y)=f(x)f(y)f(xy)$ for all $x,y \in \mathbb{R}$

Published on 01 Apr 2020 - 16:36

112

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Assumption of polynomial

Published on 25 Mar 2026 - 17:18

List Question

How to approach the functional equation $\frac{f(x+T)}{f(x)} = g(x)$?

Polynomial equation involving $\cos(x)$

Functional Equation $f(xf(y) + f(x)) + f(y^2) = f(x) + y(f(x+y))$

IMO 1994 problem 5

Solution of the functional equation $f(x)f(y)=f(x+y)+xy$

How to solve the equation $a(f(x))^2 - af(kx)f(x) + xf’(x) = 0$

Functional equation $ f(x) + f\left(1-\frac{1}{x}\right) = \tan^{-1}(x) $ and definite integral

Find all functions $f$ such that $f(f(x)+yz)=x+f(y)f(z)$

IMO $2011$ problem $3$, how can I prove that $f(x) = 0, \; \forall \; x \leq 0 $?

Solving Olympiad Functional equations: $f(xy)=f(x)f(y)$ and $f(x+z)=f(x)+f(z)$ for some $z\ne0$

Linear equation with two unknowns

Olympiad Functional Equation $f(xf(y))=yf(x)$

Necessary and sufficient condition for a function to be contraction

Find all $f$ such that $f(x+y)=f(x)f(y)f(xy)$ for all $x,y \in \mathbb{R}$

Assumption of polynomial

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