Question

Symmetric Functional Equation

score 98 · Answer 1 · 2026-04-08 20:11:11

98

Views

Symmetric Functional Equation

Published on 08 Apr 2026 - 20:11

score 167 · Answer 2 · 2026-04-17 08:20:47

167

Views

Functional inequality $\sqrt{f(x+y)}\leqslant\sqrt{f(x)}+\sqrt{f(y)}$

Published on 17 Apr 2026 - 8:20

score 66 · Answer 3 · 2026-04-12 10:52:43

66

Views

Can we characterize functions, like exponentials, the gamma function, and tetration, as solutions of an optimization problem?

Published on 12 Apr 2026 - 10:52

score 69 · Answer 4 · 2026-04-16 04:38:12

69

Views

The only continuous functions satisfying $f(x+y)f(x-y)=f(x)^2f(y)^2$ are $f\equiv-1,0,1$ - solution verification

Published on 16 Apr 2026 - 4:38

score 96 · Answer 5 · 2026-04-17 05:07:16

96

Views

Is the only continuous nonzero solution to $f(x^2-y^2)=f(x)^2-f(y)^2$ $f(x)=x$? Difficulty identifying solutions

Published on 17 Apr 2026 - 5:07

score 38 · Answer 6 · 2026-04-15 17:49:54

38

Views

Solution verification: Prove that the set is open in $C[0,1]$

Published on 15 Apr 2026 - 17:49

score 106 · Answer 7 · 2026-04-14 17:19:06

106

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finding all continuous functions $f$ so that $f(f(x)) - 2f(x) + x = 0$ for all $x\in \mathbb{R}$

Published on 14 Apr 2026 - 17:19

score 48 · Answer 8 · 2026-04-16 22:52:14

48

Views

Find $f(3)$ if $f(f(x) - y) = f(x) + f(f(y) - f(-x)) + x$

Published on 16 Apr 2026 - 22:52

score 62 · Answer 9 · 2026-04-12 15:54:41

62

Views

If an ODE depends on $f \in C^{\infty}(I, \mathbb{R})$ but not on $f'$, does the same hold for its solution?

Published on 12 Apr 2026 - 15:54

score 89 · Answer 10 · 2026-04-18 22:57:09

89

Views

Rotationally invariant function after tensorizing

Published on 18 Apr 2026 - 22:57

score 45 · Answer 11 · 2026-04-13 04:16:42

45

Views

Finding integrand that represents fraction of two integrals

Published on 13 Apr 2026 - 4:16

score 110 · Answer 12 · 2026-04-14 05:02:53

110

Views

Which even function $f(x)$ satisfies $\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)\cos(nx)~dx=\frac{1}{n}$?

Published on 14 Apr 2026 - 5:02

score 507 · Answer 13 · 2026-04-15 18:50:02

507

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Find all the functions $f:\mathbb{Z}^+ \to \mathbb{Z}^+$ such that $f(f(x)) = 15x-2f(x)+48$.

Published on 15 Apr 2026 - 18:50

score 57 · Answer 14 · 2026-04-12 23:49:17

57

Views

Non constant solutions of the following equation

Published on 12 Apr 2026 - 23:49

score 32 · Answer 15 · 2026-04-09 11:26:50

32

Views

Solution of translation functional equation

Published on 09 Apr 2026 - 11:26

List Question

Symmetric Functional Equation

Functional inequality $\sqrt{f(x+y)}\leqslant\sqrt{f(x)}+\sqrt{f(y)}$

Can we characterize functions, like exponentials, the gamma function, and tetration, as solutions of an optimization problem?

The only continuous functions satisfying $f(x+y)f(x-y)=f(x)^2f(y)^2$ are $f\equiv-1,0,1$ - solution verification

Is the only continuous nonzero solution to $f(x^2-y^2)=f(x)^2-f(y)^2$ $f(x)=x$? Difficulty identifying solutions

Solution verification: Prove that the set is open in $C[0,1]$

finding all continuous functions $f$ so that $f(f(x)) - 2f(x) + x = 0$ for all $x\in \mathbb{R}$

Find $f(3)$ if $f(f(x) - y) = f(x) + f(f(y) - f(-x)) + x$

If an ODE depends on $f \in C^{\infty}(I, \mathbb{R})$ but not on $f'$, does the same hold for its solution?

Rotationally invariant function after tensorizing

Finding integrand that represents fraction of two integrals

Which even function $f(x)$ satisfies $\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)\cos(nx)~dx=\frac{1}{n}$?

Find all the functions $f:\mathbb{Z}^+ \to \mathbb{Z}^+$ such that $f(f(x)) = 15x-2f(x)+48$.

Non constant solutions of the following equation

Solution of translation functional equation

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