Question

Functional equation $\big(\frac{1}{x}-1\big)f(x)+\big(\frac{1}{x^{\phi-1}}-1\big)f(x^\phi)=1$

score 146 · Answer 1 · 2019-12-27 13:46:10

146

Views

Functional equation $\big(\frac{1}{x}-1\big)f(x)+\big(\frac{1}{x^{\phi-1}}-1\big)f(x^\phi)=1$

Published on 27 Dec 2019 - 13:46

score 93 · Answer 2 · 2019-12-28 22:16:05

93

Views

Solving the functional equation $\sum f(n) = \sum [f(n)]^2$.

Published on 28 Dec 2019 - 22:16

score 23 · Answer 3 · 2019-12-29 16:17:17

23

Views

Need explanation on a solution of a functional equation

Published on 29 Dec 2019 - 16:17

score 33 · Answer 4 · 2019-12-31 05:18:04

33

Views

If $f: R \to R$ is a non constant, thrice differentiable function such that $f(1+ \frac{1}{n}) = 1$ for all integers, then find $f''(1)$

Published on 31 Dec 2019 - 5:18

score 671 · Answer 5 · 2026-03-17 22:59:52

671

Views

How to understand quasi-inverse of a function f∘g∘f = f?

Published on 17 Mar 2026 - 22:59

score 76 · Answer 6 · 2026-03-28 15:11:27

76

Views

Books or Notes that explain the importance of functional equations.

Published on 28 Mar 2026 - 15:11

score 89 · Answer 7 · 2026-03-26 09:47:40

89

Views

What are functions on tuples called for which $f(a,b)=f(f(a),f(b))$?

Published on 26 Mar 2026 - 9:47

score 496 · Answer 8 · 2020-01-05 16:33:37

496

Views

Proof that $a^x$ is the only solution of $f(x+y)=f(x)f(y)$

Published on 05 Jan 2020 - 16:33

score 86 · Answer 9 · 2020-01-05 17:56:52

86

Views

A certain proof that $e^{z}$ is the only solution of $f'(z)=f(z), \, f(0)=1,\, z\in\mathbb{C}$

Published on 05 Jan 2020 - 17:56

score 145 · Answer 10 · 2020-01-06 20:20:33

145

Views

Find al continuous functions $f:[0,1]\to \mathbb{R}$ such that $f(x) f(1-x) \ge \int_0^1 (f^2(x)-f(x)f(1-x)+f^2(1-x)) dx, \forall x\in [0,1]$

Published on 06 Jan 2020 - 20:20

score 83 · Answer 11 · 2026-03-27 14:52:50

83

Views

Deducing the gradient of the functional $L(\gamma)=\int_0^1\|\gamma'(s)\|\ \mathrm ds$ is of the form $\nabla L(s)=-\kappa(s)\nu(s)$

Published on 27 Mar 2026 - 14:52

score 71 · Answer 12 · 2020-01-09 09:14:40

71

Views

Find all real-valued functions $f$ satisfying $f(2x+f(y))+f(f(y))=4x+8y$

Published on 09 Jan 2020 - 9:14

score 177 · Answer 13 · 2026-03-25 15:41:17

177

Views

Solutions to $\prod_{n=1}^\infty \left ( 1+ \frac1{f(n)} \right ) = \varphi$

Published on 25 Mar 2026 - 15:41

score 46 · Answer 14 · 2020-01-13 07:50:04

46

Views

On the equation $f(x^2+y+f(y))=2y+f(x)^2.$

Published on 13 Jan 2020 - 7:50

score 79 · Answer 15 · 2026-03-28 11:33:28

79

Views

solution of fuctional equation: $f(g(x))=x^2$.

Published on 28 Mar 2026 - 11:33

List Question

Functional equation $\big(\frac{1}{x}-1\big)f(x)+\big(\frac{1}{x^{\phi-1}}-1\big)f(x^\phi)=1$

Solving the functional equation $\sum f(n) = \sum [f(n)]^2$.

Need explanation on a solution of a functional equation

If $f: R \to R$ is a non constant, thrice differentiable function such that $f(1+ \frac{1}{n}) = 1$ for all integers, then find $f''(1)$

How to understand quasi-inverse of a function f∘g∘f = f?

Books or Notes that explain the importance of functional equations.

What are functions on tuples called for which $f(a,b)=f(f(a),f(b))$?

Proof that $a^x$ is the only solution of $f(x+y)=f(x)f(y)$

A certain proof that $e^{z}$ is the only solution of $f'(z)=f(z), \, f(0)=1,\, z\in\mathbb{C}$

Find al continuous functions $f:[0,1]\to \mathbb{R}$ such that $f(x) f(1-x) \ge \int_0^1 (f^2(x)-f(x)f(1-x)+f^2(1-x)) dx, \forall x\in [0,1]$

Deducing the gradient of the functional $L(\gamma)=\int_0^1\|\gamma'(s)\|\ \mathrm ds$ is of the form $\nabla L(s)=-\kappa(s)\nu(s)$

Find all real-valued functions $f$ satisfying $f(2x+f(y))+f(f(y))=4x+8y$

Solutions to $\prod_{n=1}^\infty \left ( 1+ \frac1{f(n)} \right ) = \varphi$

On the equation $f(x^2+y+f(y))=2y+f(x)^2.$

solution of fuctional equation: $f(g(x))=x^2$.

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