Question

Pexider's (/ Cauchy's) functional equation over a bounded domain

score 186 · Answer 1 · 2018-11-14 20:22:51

186

Views

Pexider's (/ Cauchy's) functional equation over a bounded domain

Published on 14 Nov 2018 - 20:22

score 81 · Answer 2 · 2018-11-17 18:07:09

81

Views

Find a strictly decreasing $f:(0,1) \to [0, \infty]$ such that $f(0^{+})= \infty$, $f(1)=0$ and $f(u^2)=2 f(u)$.

Published on 17 Nov 2018 - 18:07

score 45 · Answer 3 · 2026-03-25 03:18:11

45

Views

First Variation of CDF inside an Indicator Function

Published on 25 Mar 2026 - 3:18

score 179 · Answer 4 · 2018-11-22 02:22:25

179

Views

Is there a continuous $f$ satisfying $f(f(x))=-x^3+x$?

Published on 22 Nov 2018 - 2:22

score 321 · Answer 5 · 2018-11-22 13:47:33

321

Views

$f(y+zf(x))=f(y)+xf(z) $ with $x,y,z\in \mathbb{R}$

Published on 22 Nov 2018 - 13:47

score 74 · Answer 6 · 2026-03-25 01:21:43

74

Views

An inequality involving the Dirichlet eta function

Published on 25 Mar 2026 - 1:21

score 84 · Answer 7 · 2026-03-25 14:25:51

84

Views

How is it possible to minimize a definite integral, if there are three parameters that can be varied in the integrand?

Published on 25 Mar 2026 - 14:25

score 64 · Answer 8 · 2018-11-25 16:44:55

64

Views

$G(x,y)G(y,z)$ independant of $y$ $\implies$ Most general function form $G(x,y) = rH(x)/H(y)$ , $r$ a const.

Published on 25 Nov 2018 - 16:44

score 135 · Answer 9 · 2018-11-25 18:47:53

135

Views

Functions satisfying $f(a+b) =\frac{f(a)+f(b)}{f(a)*f(b)}$

Published on 25 Nov 2018 - 18:47

score 167 · Answer 10 · 2026-03-25 04:43:52

167

Views

Determine all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that, for every positive integer $n$, we have: $2n+2001≤f(f(n))+f(n)≤2n+2002$.

Published on 25 Mar 2026 - 4:43

score 260 · Answer 11 · 2018-11-26 21:13:48

260

Views

Find function $f$ given $f(x+1) - f(x) = \frac{1}{x^2}$

Published on 26 Nov 2018 - 21:13

score 374 · Answer 12 · 2018-11-27 14:13:06

374

Views

Polynomials $P(x)\in k[x]$ satisfying condition $P(x^2)=P(-x)P(x)$

Published on 27 Nov 2018 - 14:13

score 69 · Answer 13 · 2018-11-30 04:36:59

69

Views

Find all real functions satisfying $ f \big( y - f ( x ) \big) = f \left( x ^ { 2002 } - y \right) - 2001 y f ( x ) $

Published on 30 Nov 2018 - 4:36

score 65 · Answer 14 · 2018-12-01 06:30:51

65

Views

Problem in solving the functional equation $f(x-y)=f(x)f(y)+g(x)g(y)$

Published on 01 Dec 2018 - 6:30

score 91 · Answer 15 · 2018-12-01 16:04:55

91

Views

Is there a function that satisfies $f(\log \frac{p}{1-p}) = p(1-p)$?

Published on 01 Dec 2018 - 16:04

List Question

Pexider's (/ Cauchy's) functional equation over a bounded domain

Find a strictly decreasing $f:(0,1) \to [0, \infty]$ such that $f(0^{+})= \infty$, $f(1)=0$ and $f(u^2)=2 f(u)$.

First Variation of CDF inside an Indicator Function

Is there a continuous $f$ satisfying $f(f(x))=-x^3+x$?

$f(y+zf(x))=f(y)+xf(z) $ with $x,y,z\in \mathbb{R}$

An inequality involving the Dirichlet eta function

How is it possible to minimize a definite integral, if there are three parameters that can be varied in the integrand?

$G(x,y)G(y,z)$ independant of $y$ $\implies$ Most general function form $G(x,y) = rH(x)/H(y)$ , $r$ a const.

Functions satisfying $f(a+b) =\frac{f(a)+f(b)}{f(a)*f(b)}$

Determine all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that, for every positive integer $n$, we have: $2n+2001≤f(f(n))+f(n)≤2n+2002$.

Find function $f$ given $f(x+1) - f(x) = \frac{1}{x^2}$

Polynomials $P(x)\in k[x]$ satisfying condition $P(x^2)=P(-x)P(x)$

Find all real functions satisfying $ f \big( y - f ( x ) \big) = f \left( x ^ { 2002 } - y \right) - 2001 y f ( x ) $

Problem in solving the functional equation $f(x-y)=f(x)f(y)+g(x)g(y)$

Is there a function that satisfies $f(\log \frac{p}{1-p}) = p(1-p)$?

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