Question

Any solutions to the functional equation $f(x) = f(x-1)-f(x+1)-ix^3f(x)$?

score 106 · Answer 1 · 2017-04-28 16:29:36

106

Views

Any solutions to the functional equation $f(x) = f(x-1)-f(x+1)-ix^3f(x)$?

Published on 28 Apr 2017 - 16:29

score 33 · Answer 2 · 2026-03-25 16:40:12

33

Views

Is 1 point homogeinety (essentially) , with F(1)=1; F:[0,1]\to[0,1], equivalent to, Cauchy's equation and continuity, by itself?

Published on 25 Mar 2026 - 16:40

score 166 · Answer 3 · 2017-04-29 13:55:45

Find the sum of all values of $ f ( 2017 ) $ given $ f ^ { f ( a ) } ( b ) f ^ { f ( b ) } ( a ) = f ( a + b ) ^ 2 $.

score 290 · Answer 4 · 2017-04-30 05:47:15

290

Views

Functional equation: $f(f(x)) = e^x$

Published on 30 Apr 2017 - 5:47

score 57 · Answer 5 · 2017-05-02 04:55:41

57

Views

$\boxed{1} f(x)=\frac{2-x^2}{2}f(\frac{2-x^2}{2})$

Published on 02 May 2017 - 4:55

score 193 · Answer 6 · 2017-05-02 12:06:33

193

Views

Functional equations $f\left(\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}$ and $f(x)=\frac{f\left(\frac{2}{3}x\right)+f\left(\frac{4}{3}x\right)}{2}$.

Published on 02 May 2017 - 12:06

score 388 · Answer 7 · 2026-04-06 13:10:39

388

Views

What is the equation of Species Accumulation Curve?

Published on 06 Apr 2026 - 13:10

score 249 · Answer 8 · 2026-03-30 09:51:16

249

Views

Suppose $a+b+c+d=s$ and $1/a+1/b+1/c+1/d=s$, how can you make any possible conclusions?

Published on 30 Mar 2026 - 9:51

score 130 · Answer 9 · 2026-03-31 20:10:30

Solve the functional equation $f(4x(1-x))=\sin(\pi f(x))$ for find an invariant measure of a dynamical system $x_{n+1}=\sin(\pi x_{n})$

score 208 · Answer 10 · 2017-05-03 22:46:17

208

Views

Sufficient conditions for the Schroder functional equation

Published on 03 May 2017 - 22:46

score 869 · Answer 11 · 2026-03-26 13:50:45

869

Views

Elementary Symmetric functions of one variable

Published on 26 Mar 2026 - 13:50

score 8.8k · Answer 12 · 2017-05-04 17:26:43

8.8k

Views

Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$

Published on 04 May 2017 - 17:26

score 36 · Answer 13 · 2026-03-26 16:10:19

36

Views

What assumptions do we need on $f$ and $g$ for the equation $Df = f+g$ to be solveable in this way?

Published on 26 Mar 2026 - 16:10

score 284 · Answer 14 · 2017-05-05 20:51:43

284

Views

Functional equation using Hamel basis

Published on 05 May 2017 - 20:51

score 29 · Answer 15 · 2026-03-25 12:52:20

29

Views

Concluding Even-ness From a Simple Functional Identity

Published on 25 Mar 2026 - 12:52

List Question

Any solutions to the functional equation $f(x) = f(x-1)-f(x+1)-ix^3f(x)$?

Is 1 point homogeinety (essentially) , with F(1)=1; F:[0,1]\to[0,1], equivalent to, Cauchy's equation and continuity, by itself?

Find the sum of all values of $ f ( 2017 ) $ given $ f ^ { f ( a ) } ( b ) f ^ { f ( b ) } ( a ) = f ( a + b ) ^ 2 $.

Functional equation: $f(f(x)) = e^x$

$\boxed{1} f(x)=\frac{2-x^2}{2}f(\frac{2-x^2}{2})$

Functional equations $f\left(\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}$ and $f(x)=\frac{f\left(\frac{2}{3}x\right)+f\left(\frac{4}{3}x\right)}{2}$.

What is the equation of Species Accumulation Curve?

Suppose $a+b+c+d=s$ and $1/a+1/b+1/c+1/d=s$, how can you make any possible conclusions?

Solve the functional equation $f(4x(1-x))=\sin(\pi f(x))$ for find an invariant measure of a dynamical system $x_{n+1}=\sin(\pi x_{n})$

Sufficient conditions for the Schroder functional equation

Elementary Symmetric functions of one variable

Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$

What assumptions do we need on $f$ and $g$ for the equation $Df = f+g$ to be solveable in this way?

Functional equation using Hamel basis

Concluding Even-ness From a Simple Functional Identity

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