List questions from functional-equations

278

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Find all pairs of functions $(f,g)$, $\forall x, y \in \mathbb{R}, f(x+g(y))=x f(y) - y f(x) + g(x)$

Published on 29 Mar 2014 - 14:27

374

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How find this function $f(x)$ such $f(a+f(b))=f(a+b)+f(b)$

Published on 31 Mar 2014 - 14:36

612

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$1992$ IMO Functional Equation problem

Published on 01 Apr 2014 - 17:36

7.1k

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Function whose inverse is also its derivative?

Published on 01 Apr 2014 - 21:00

95

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$f(x)=xf(1)$ Doubt

Published on 03 Apr 2014 - 0:35

66

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The uniqueness of a solution of a system of differential equations

Published on 04 Apr 2014 - 8:10

175

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Is this a field of study?

Published on 04 Apr 2014 - 22:05

3.8k

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If $f:\mathbb N\to\mathbb N$ such that $f\big(f(x)\big)=3x$, then find $f(2013)$.

Published on 05 Apr 2014 - 10:32

167

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Solve the functional equation, $f(x+y+1)= \left(\sqrt{f(x)} + \sqrt{f(y)}\right)^2$

Published on 07 Apr 2014 - 5:15

2.4k

Views

if $f(mn)+f(m+n-1)=f(m)f(n)$How find $f(n)$

Published on 07 Apr 2014 - 17:19

75

Views

Wronskian different from zero and solutions of ODE.

Published on 09 Apr 2014 - 22:39

579

Views

Contour approach to Riemann zeta functional equation

Published on 11 Apr 2014 - 15:04

85

Views

Creating a monotonic function

Published on 11 Apr 2014 - 18:18

160

Views

Solving the functional equation $(x+1)f\left(\frac{y}{f(x)}\right)=f(x+y)$

Published on 12 Apr 2014 - 3:14

51

Views

Functional Equation and totally multiplicative functions

Published on 13 Apr 2014 - 1:40

List Question

Find all pairs of functions $(f,g)$, $\forall x, y \in \mathbb{R}, f(x+g(y))=x f(y) - y f(x) + g(x)$

How find this function $f(x)$ such $f(a+f(b))=f(a+b)+f(b)$

$1992$ IMO Functional Equation problem

Function whose inverse is also its derivative?

$f(x)=xf(1)$ Doubt

The uniqueness of a solution of a system of differential equations

Is this a field of study?

If $f:\mathbb N\to\mathbb N$ such that $f\big(f(x)\big)=3x$, then find $f(2013)$.

Solve the functional equation, $f(x+y+1)= \left(\sqrt{f(x)} + \sqrt{f(y)}\right)^2$

if $f(mn)+f(m+n-1)=f(m)f(n)$How find $f(n)$

Wronskian different from zero and solutions of ODE.

Contour approach to Riemann zeta functional equation

Creating a monotonic function

Solving the functional equation $(x+1)f\left(\frac{y}{f(x)}\right)=f(x+y)$

Functional Equation and totally multiplicative functions

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