Question

Functional equation problem; chain of functions

score 110 · Answer 1 · 2019-07-25 14:43:46

110

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Functional equation problem; chain of functions

Published on 25 Jul 2019 - 14:43

score 91 · Answer 2 · 2019-07-25 17:18:09

91

Views

System of functional equations $ f(f(x)-f(y))=|f(x)-f(y)|, \; f(1-f(x+2))=1-f(x)$

Published on 25 Jul 2019 - 17:18

score 1.5k · Answer 3 · 2019-07-27 19:45:26

1.5k

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Finding $f$ such that $f(f(f(f...(x)))) = x$

Published on 27 Jul 2019 - 19:45

score 77 · Answer 4 · 2019-07-28 10:38:47

77

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Find all functions $f\colon\Bbb R\to \Bbb R$ that satisfy $|f(x)-f(y)| =3|x-y|$ for all $x,y \in \mathbb{R}$.

Published on 28 Jul 2019 - 10:38

score 172 · Answer 5 · 2019-07-30 10:33:25

172

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If $f: \mathbb R^n \to \mathbb R^n$ satisfies $\|f(x - y)\| = \|f(x) - f(y)\|$, is $f$ additive?

Published on 30 Jul 2019 - 10:33

score 245 · Answer 6 · 2019-07-30 10:35:43

245

Views

$h(x,y)=f(x)+g(y)$

Published on 30 Jul 2019 - 10:35

score 77 · Answer 7 · 2019-07-31 11:51:48

Show that the functional equation $f(f(x))=-x^{3}+g(x)$ has no continuous solution.Here $g$ is a continuous periodic function with positive period.

score 52 · Answer 8 · 2019-08-01 16:58:18

52

Views

Functional inequation

Published on 01 Aug 2019 - 16:58

score 65 · Answer 9 · 2019-08-02 16:23:49

65

Views

How to find the solutions of this functional equation

Published on 02 Aug 2019 - 16:23

score 742 · Answer 10 · 2019-08-02 18:19:35

742

Views

If $f(xy) = f(x)+f(y)+xy-x-y$ and $f'(1)=4$, evaluate $f$

Published on 02 Aug 2019 - 18:19

score 115 · Answer 11 · 2019-08-03 06:25:32

115

Views

Proof of Theorem 1, Calulus of Variation, Gelfand and Fomin

Published on 03 Aug 2019 - 6:25

score 324 · Answer 12 · 2019-08-03 17:32:44

324

Views

Questions about the existence of a function

Published on 03 Aug 2019 - 17:32

score 69 · Answer 13 · 2019-08-03 20:02:02

69

Views

Proving ideal gas equation from Boyle’s, Charles’ and Gay-Lussac’s laws

Published on 03 Aug 2019 - 20:02

score 369 · Answer 14 · 2019-08-04 09:40:45

369

Views

Existence of function satisfying $f(f'(x))=x$ almost everywhere

Published on 04 Aug 2019 - 9:40

score 224 · Answer 15 · 2019-08-07 06:48:16

224

Views

What are all the functions that satisfy $f(x)/f(y) = f(kx)/f(ky)$?

Published on 07 Aug 2019 - 6:48

List Question

Functional equation problem; chain of functions

System of functional equations $ f(f(x)-f(y))=|f(x)-f(y)|, \; f(1-f(x+2))=1-f(x)$

Finding $f$ such that $f(f(f(f...(x)))) = x$

Find all functions $f\colon\Bbb R\to \Bbb R$ that satisfy $|f(x)-f(y)| =3|x-y|$ for all $x,y \in \mathbb{R}$.

If $f: \mathbb R^n \to \mathbb R^n$ satisfies $\|f(x - y)\| = \|f(x) - f(y)\|$, is $f$ additive?

$h(x,y)=f(x)+g(y)$

Show that the functional equation $f(f(x))=-x^{3}+g(x)$ has no continuous solution.Here $g$ is a continuous periodic function with positive period.

Functional inequation

How to find the solutions of this functional equation

If $f(xy) = f(x)+f(y)+xy-x-y$ and $f'(1)=4$, evaluate $f$

Proof of Theorem 1, Calulus of Variation, Gelfand and Fomin

Questions about the existence of a function

Proving ideal gas equation from Boyle’s, Charles’ and Gay-Lussac’s laws

Existence of function satisfying $f(f'(x))=x$ almost everywhere

What are all the functions that satisfy $f(x)/f(y) = f(kx)/f(ky)$?

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