List questions from functional-equations

Published on 07 Jan 2015 - 13:58

196

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What is derivative a of a continuous function such that $f(x+y) = f(x) +f(y)$?

Published on 08 Jan 2015 - 8:22

63

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Functions that hasn't any root

Published on 08 Jan 2015 - 12:00

354

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Functional Equation $f(f'(x))=-f(x)$

Published on 08 Jan 2015 - 19:59

96

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Entire $f,g$ such that $f(f(z)) = p(g(z))$

Published on 26 Mar 2026 - 6:08

48

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Is this a valid equivalence between the classes of Differential Equations?

Published on 09 Jan 2015 - 11:46

432

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Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$

Published on 09 Jan 2015 - 17:41

94

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Problem in Putnum competition?

Published on 10 Jan 2015 - 18:08

125

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Is $T:C[0,1]\to C[0,1]: Tf(x)=\frac12 x f(x^2)+1$ a contraction?

Published on 12 Jan 2015 - 17:07

77

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Is there a $f\in C[0,1]$ such that $f(x)=\frac12 \sin (f(1-x))$

Published on 12 Jan 2015 - 20:51

164

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Existence solution pendulum equation using the contraction principle

Published on 12 Jan 2015 - 22:13

35

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Proving that $(Sf)(x)=1+\int_0^x t^2f(t)\,dt$ is $K$-Lipschitz

Published on 25 Mar 2026 - 9:27

40

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Is $Tf=x_0+\int_0^tf(t)(1-f)\,dt$ a Lipschitz function?

Published on 13 Jan 2015 - 7:41

110

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A functional equation involving convolution

Published on 02 Apr 2026 - 15:32

28.6k

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To find an extremal of the functional $\int_0^1 [(y')^2 + 12 xy] dx$

Published on 02 Apr 2026 - 13:26

List Question

Find all real functions so that $f(xf(y)+f(x))=f(yf(x))+x$

What is derivative a of a continuous function such that $f(x+y) = f(x) +f(y)$?

Functions that hasn't any root

Functional Equation $f(f'(x))=-f(x)$

Entire $f,g$ such that $f(f(z)) = p(g(z))$

Is this a valid equivalence between the classes of Differential Equations?

Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$

Problem in Putnum competition?

Is $T:C[0,1]\to C[0,1]: Tf(x)=\frac12 x f(x^2)+1$ a contraction?

Is there a $f\in C[0,1]$ such that $f(x)=\frac12 \sin (f(1-x))$

Existence solution pendulum equation using the contraction principle

Proving that $(Sf)(x)=1+\int_0^x t^2f(t)\,dt$ is $K$-Lipschitz

Is $Tf=x_0+\int_0^tf(t)(1-f)\,dt$ a Lipschitz function?

A functional equation involving convolution

To find an extremal of the functional $\int_0^1 [(y')^2 + 12 xy] dx$

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