Question

Functional differential equation for the Fabius function

score 63 · Answer 1 · 2026-04-12 06:11:14

63

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Functional differential equation for the Fabius function

Published on 12 Apr 2026 - 6:11

score 72 · Answer 2 · 2021-01-06 00:27:08

72

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$f:\Bbb R\mapsto\Bbb R$ such that $f(x+y)f(x-y)=2x+f(x^2-y^2)$

Published on 06 Jan 2021 - 0:27

score 64 · Answer 3 · 2021-01-06 17:32:10

64

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Finding $f \colon R_+ \to R_+$ such that $sf = f \circ g$, for $g$ strictly increasing

Published on 06 Jan 2021 - 17:32

score 180 · Answer 4 · 2021-01-07 00:42:02

180

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Numerical method for functional equations similar to $2f(x) - f(x+2) - f(x-2) = 0$

Published on 07 Jan 2021 - 0:42

score 43 · Answer 5 · 2021-01-12 06:38:01

43

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How to find $f(x)$ such that $f(y)-f(x)-(y-x)f'(\frac{x+y}{2})+\frac{(x-y)^2}{4}=0$

Published on 12 Jan 2021 - 6:38

score 47 · Answer 6 · 2026-04-12 17:51:23

47

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Finding all the functions satisfying particular conditions.

Published on 12 Apr 2026 - 17:51

score 84 · Answer 7 · 2021-01-14 00:17:20

84

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Find all functions $f(x^2-y^2)=f(xy)(f(x)+f(y))$

Published on 14 Jan 2021 - 0:17

score 141 · Answer 8 · 2021-01-14 01:11:45

141

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Functions $f:\mathbb Z^2\to\mathbb R$ with $f(x,y)=\frac{f(x-1,y)+f(x,y-1)}{2}$

Published on 14 Jan 2021 - 1:11

score 57 · Answer 9 · 2026-04-11 20:12:34

57

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Variational calculus for functional equation results in under-determined system.

Published on 11 Apr 2026 - 20:12

score 188 · Answer 10 · 2021-01-15 05:36:22

188

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Inequality concerning a function :${(f(x))}^2=1+xf(x+1)$

Published on 15 Jan 2021 - 5:36

score 442 · Answer 11 · 2021-01-15 21:41:50

442

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Finishing the solution to this functional equation: $ f\left(x^2+y\right)=f\bigl(f(x)-y\bigr) + 4f(x)y $

Published on 15 Jan 2021 - 21:41

score 222 · Answer 12 · 2021-01-16 06:24:17

222

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If $f$ is a uniformly continuous function on a metric vector space, is there a continuous $g$ with $f=e^{{\rm i}g}$?

Published on 16 Jan 2021 - 6:24

score 202 · Answer 13 · 2026-04-12 21:11:16

202

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The functional equation $\delta(n) = \delta(2n) + \kappa(n)$

Published on 12 Apr 2026 - 21:11

score 164 · Answer 14 · 2026-04-13 07:50:01

164

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A functional equation while attempting to integrate a function differently: $ f(x)-f(y) = z \bigl( f(xz) - f(yz) \bigr) $

Published on 13 Apr 2026 - 7:50

score 25 · Answer 15 · 2021-01-23 14:15:50

25

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If $f(a;f(b;c)) = f(a;b) + c$ and $f(a;a) = 0$ , then find $f($1.1$; -5)$

Published on 23 Jan 2021 - 14:15

List Question

Functional differential equation for the Fabius function

$f:\Bbb R\mapsto\Bbb R$ such that $f(x+y)f(x-y)=2x+f(x^2-y^2)$

Finding $f \colon R_+ \to R_+$ such that $sf = f \circ g$, for $g$ strictly increasing

Numerical method for functional equations similar to $2f(x) - f(x+2) - f(x-2) = 0$

How to find $f(x)$ such that $f(y)-f(x)-(y-x)f'(\frac{x+y}{2})+\frac{(x-y)^2}{4}=0$

Finding all the functions satisfying particular conditions.

Find all functions $f(x^2-y^2)=f(xy)(f(x)+f(y))$

Functions $f:\mathbb Z^2\to\mathbb R$ with $f(x,y)=\frac{f(x-1,y)+f(x,y-1)}{2}$

Variational calculus for functional equation results in under-determined system.

Inequality concerning a function :${(f(x))}^2=1+xf(x+1)$

Finishing the solution to this functional equation: $ f\left(x^2+y\right)=f\bigl(f(x)-y\bigr) + 4f(x)y $

If $f$ is a uniformly continuous function on a metric vector space, is there a continuous $g$ with $f=e^{{\rm i}g}$?

The functional equation $\delta(n) = \delta(2n) + \kappa(n)$

A functional equation while attempting to integrate a function differently: $ f(x)-f(y) = z \bigl( f(xz) - f(yz) \bigr) $

If $f(a;f(b;c)) = f(a;b) + c$ and $f(a;a) = 0$ , then find $f($1.1$; -5)$

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