List questions from functional-equations

Published on 02 May 2015 - 20:20

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Functional equation $f(f(x))=2x$ on $\mathbb{Z}_{>0}$

Published on 03 May 2015 - 19:33

1.4k

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Suppose $f$ is a real function satisfying $f(x+f(x))$ = $4f(x)$ and $f(1) = 4$. Then the value of $f(21)$?

Published on 04 May 2015 - 17:56

105

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Prove equation using taylor series

Published on 08 May 2015 - 8:35

62

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Solving a particular Functional Differential Equation

Published on 08 May 2015 - 18:40

220

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Functional equation $f'(x)=cf(x+1)$ has a solution if and only if $c\leq 1/e$

Published on 08 May 2015 - 20:25

267

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How do I prove this function is monotonic?

Published on 11 May 2015 - 0:43

101

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Solve: $f(x+\frac{1}{y}) + f(x-\frac{1}{y}) = 2f(x).f(\frac{1}{y})$

Published on 12 May 2015 - 5:04

102

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Pexerized D'alembert functional equation $f(x+y)+g(x−y)=\lambda f(x)g(y)$

Published on 12 May 2015 - 15:12

141

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Cauchy's function

Published on 13 May 2015 - 13:46

352

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Proof regarding a probability generating function (Poisson)

Published on 14 May 2015 - 0:20

190

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Solving the functional equation $f(x + y) + g(x-y) = \lambda g(x) f(y)$

Published on 14 May 2015 - 16:50

112

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Trigonometric functional equation $g(x)f(y) = f \left(\frac{x + y}{2}\right)^2-f\left(\frac{x-y}{2}\right)^2$

Published on 15 May 2015 - 17:42

1.1k

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What function satisfies $f(x)+f(−x)=f(x^2)$?

Published on 15 May 2015 - 20:30

1.6k

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Minimizing a functional with a free boundary condition

Published on 23 Feb 2026 - 21:11

List Question

Demonstrating solutions to two functional equations

Functional equation $f(f(x))=2x$ on $\mathbb{Z}_{>0}$

Suppose $f$ is a real function satisfying $f(x+f(x))$ = $4f(x)$ and $f(1) = 4$. Then the value of $f(21)$?

Prove equation using taylor series

Solving a particular Functional Differential Equation

Functional equation $f'(x)=cf(x+1)$ has a solution if and only if $c\leq 1/e$

How do I prove this function is monotonic?

Solve: $f(x+\frac{1}{y}) + f(x-\frac{1}{y}) = 2f(x).f(\frac{1}{y})$

Pexerized D'alembert functional equation $f(x+y)+g(x−y)=\lambda f(x)g(y)$

Cauchy's function

Proof regarding a probability generating function (Poisson)

Solving the functional equation $f(x + y) + g(x-y) = \lambda g(x) f(y)$

Trigonometric functional equation $g(x)f(y) = f \left(\frac{x + y}{2}\right)^2-f\left(\frac{x-y}{2}\right)^2$

What function satisfies $f(x)+f(−x)=f(x^2)$?

Minimizing a functional with a free boundary condition

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