Question

Functions over $\mathbb C$ that are both additive and multiplicative

score 183 · Answer 1 · 2020-01-28 21:46:25

183

Views

Functions over $\mathbb C$ that are both additive and multiplicative

Published on 28 Jan 2020 - 21:46

score 130 · Answer 2 · 2020-01-29 14:07:58

130

Views

Basic Functional equation $f\left(\sqrt{\frac{x^2+y^2}{2}}\right)=\sqrt{f(x)\cdot f(y)},\;\forall x,y\geq0$

Published on 29 Jan 2020 - 14:07

score 118 · Answer 3 · 2020-02-02 14:31:36

118

Views

Prove that $\lim_{h\to 0}\frac{e^h-1}{h}=1$ from the functional equation $f(x+y)=f(x)f(y)$.

Published on 02 Feb 2020 - 14:31

score 70 · Answer 4 · 2026-03-29 08:44:41

70

Views

Calculate the fixed field of these automorphisms

Published on 29 Mar 2026 - 8:44

score 276 · Answer 5 · 2020-02-06 12:58:32

276

Views

suppose a function $f$ satisfies the equation $f(x+y)=f(x)+f(y)+xy^2+yx^2$

Published on 06 Feb 2020 - 12:58

score 132 · Answer 6 · 2020-02-08 12:17:41

132

Views

function equation $f(x)+f(y)=f(\frac {x+y} {1+xy})$

Published on 08 Feb 2020 - 12:17

score 1.6k · Answer 7 · 2020-02-08 23:52:31

1.6k

Views

$f(3x+2y)=f(x)f(y)$ for all $x,y \in \mathbb{N}.$

Published on 08 Feb 2020 - 23:52

score 78 · Answer 8 · 2020-02-09 16:43:00

78

Views

About $T(n^2) = T^2(n)/n$, with a point defined in $T(p) = q$.

Published on 09 Feb 2020 - 16:43

score 214 · Answer 9 · 2026-03-25 15:53:00

214

Views

$\frac{(x-y)^3}{x+y}\neq g(f(x)-f(y))$?

Published on 25 Mar 2026 - 15:53

score 713 · Answer 10 · 2020-02-15 16:15:17

713

Views

Does there exist a continuous function $f$ such that $f(x)+f(x^2)=x$ for $x\in[0,1]$?

Published on 15 Feb 2020 - 16:15

score 94 · Answer 11 · 2020-02-16 17:42:23

94

Views

finding an explicit solution to a functional equation

Published on 16 Feb 2020 - 17:42

score 65 · Answer 12 · 2020-02-17 07:12:11

65

Views

$\phi(x)=f(x)/g(x)$. Then $\phi(x)=h(f(x))$ if and only if $g(x)=\psi(f(x))$ for some function $psi$?

Published on 17 Feb 2020 - 7:12

score 70 · Answer 13 · 2026-03-28 07:51:44

70

Views

Legendre Transformation of the functional $F=(\phi(x))^n$

Published on 28 Mar 2026 - 7:51

score 34 · Answer 14 · 2026-03-26 14:23:02

34

Views

How to maximize a functional of the form $g(\int_\xi L_1(x) ds,\dots, \int_\xi L_N(x) ds)$?

Published on 26 Mar 2026 - 14:23

score 96 · Answer 15 · 2026-03-28 20:37:47

96

Views

What is the value of $x$, given that $f\left(x\right)+f\left(\frac{1}{1-x}\right)=x$ and $f^{-1}\left(x\right)=2$?

Published on 28 Mar 2026 - 20:37

List Question

Functions over $\mathbb C$ that are both additive and multiplicative

Basic Functional equation $f\left(\sqrt{\frac{x^2+y^2}{2}}\right)=\sqrt{f(x)\cdot f(y)},\;\forall x,y\geq0$

Prove that $\lim_{h\to 0}\frac{e^h-1}{h}=1$ from the functional equation $f(x+y)=f(x)f(y)$.

Calculate the fixed field of these automorphisms

suppose a function $f$ satisfies the equation $f(x+y)=f(x)+f(y)+xy^2+yx^2$

function equation $f(x)+f(y)=f(\frac {x+y} {1+xy})$

$f(3x+2y)=f(x)f(y)$ for all $x,y \in \mathbb{N}.$

About $T(n^2) = T^2(n)/n$, with a point defined in $T(p) = q$.

$\frac{(x-y)^3}{x+y}\neq g(f(x)-f(y))$?

Does there exist a continuous function $f$ such that $f(x)+f(x^2)=x$ for $x\in[0,1]$?

finding an explicit solution to a functional equation

$\phi(x)=f(x)/g(x)$. Then $\phi(x)=h(f(x))$ if and only if $g(x)=\psi(f(x))$ for some function $psi$?

Legendre Transformation of the functional $F=(\phi(x))^n$

How to maximize a functional of the form $g(\int_\xi L_1(x) ds,\dots, \int_\xi L_N(x) ds)$?

What is the value of $x$, given that $f\left(x\right)+f\left(\frac{1}{1-x}\right)=x$ and $f^{-1}\left(x\right)=2$?

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