Question

Functional extrema and the Euler-Lagrange equation

score 417 · Answer 1 · 2026-03-28 08:47:12

417

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Functional extrema and the Euler-Lagrange equation

Published on 28 Mar 2026 - 8:47

score 173 · Answer 2 · 2016-05-28 03:03:55

173

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solve equations - find a short piece of a wire

Published on 28 May 2016 - 3:03

score 115 · Answer 3 · 2016-05-28 12:23:56

115

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The 'prime logarithm'

Published on 28 May 2016 - 12:23

score 68 · Answer 4 · 2016-05-28 17:45:48

68

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$f(yf(\frac{x}{y})) = \frac{x^4}{f(y)} $

Published on 28 May 2016 - 17:45

score 183 · Answer 5 · 2026-03-25 19:51:25

183

Views

Banach fixed-point theorem for a recursive functional equation

Published on 25 Mar 2026 - 19:51

score 2.1k · Answer 6 · 2016-05-30 22:14:29

2.1k

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How to solve functional equations using the given tips

Published on 30 May 2016 - 22:14

score 146 · Answer 7 · 2016-06-01 13:50:58

146

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Solving a functional equation $2 f(2x)=f(x)(1+\cos(x))+f(x+\pi)(1-\cos(x))$

Published on 01 Jun 2016 - 13:50

score 193 · Answer 8 · 2016-06-01 21:53:44

193

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Is there a function $f:\mathbb{Z}\rightarrow\mathbb{Z}$ such that $f(f(x))=x+1$?

Published on 01 Jun 2016 - 21:53

score 97 · Answer 9 · 2016-06-04 15:48:46

97

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Finding all $f:[0, \infty) \to [0, \infty)$ differentiable and convex with $f(0)=0$ and $f'(x)\cdot f\bigl(f(x)\bigr)=x$

Published on 04 Jun 2016 - 15:48

score 1.9k · Answer 10 · 2016-06-07 02:15:58

1.9k

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How to prove $f(x) = \ln x$ continuous by proving first that $f(x)$ continuous at $1$, and then by using $\ln (xy) = \ln(x) + \ln(y)$.

Published on 07 Jun 2016 - 2:15

score 241 · Answer 11 · 2016-06-07 07:10:55

241

Views

Functional equation involving sine function: $ \sin x + f ( x ) = \sqrt 2 f \left( x - \frac \pi 4 \right) $

Published on 07 Jun 2016 - 7:10

score 742 · Answer 12 · 2016-06-07 09:03:51

742

Views

Find all functions $f:\mathbb R \to \mathbb R$ satisfying $xf(y)-yf(x)=f\left( \frac yx\right)$

Published on 07 Jun 2016 - 9:03

score 16 · Answer 13 · 2016-06-07 14:03:39

16

Views

How do I determine periodicity of a function through a system of functional equations?

Published on 07 Jun 2016 - 14:03

score 2.1k · Answer 14 · 2016-06-09 08:42:27

2.1k

Views

Converting parametric function into cartesian

Published on 09 Jun 2016 - 8:42

score 72 · Answer 15 · 2026-03-27 09:48:07

72

Views

functional equation $\dfrac {x + y + xy} 2 = f \big( f^{[-1]}(x) + f^{[-1]}(y) \big)$

Published on 27 Mar 2026 - 9:48

List Question

Functional extrema and the Euler-Lagrange equation

solve equations - find a short piece of a wire

The 'prime logarithm'

$f(yf(\frac{x}{y})) = \frac{x^4}{f(y)} $

Banach fixed-point theorem for a recursive functional equation

How to solve functional equations using the given tips

Solving a functional equation $2 f(2x)=f(x)(1+\cos(x))+f(x+\pi)(1-\cos(x))$

Is there a function $f:\mathbb{Z}\rightarrow\mathbb{Z}$ such that $f(f(x))=x+1$?

Finding all $f:[0, \infty) \to [0, \infty)$ differentiable and convex with $f(0)=0$ and $f'(x)\cdot f\bigl(f(x)\bigr)=x$

How to prove $f(x) = \ln x$ continuous by proving first that $f(x)$ continuous at $1$, and then by using $\ln (xy) = \ln(x) + \ln(y)$.

Functional equation involving sine function: $ \sin x + f ( x ) = \sqrt 2 f \left( x - \frac \pi 4 \right) $

Find all functions $f:\mathbb R \to \mathbb R$ satisfying $xf(y)-yf(x)=f\left( \frac yx\right)$

How do I determine periodicity of a function through a system of functional equations?

Converting parametric function into cartesian

functional equation $\dfrac {x + y + xy} 2 = f \big( f^{[-1]}(x) + f^{[-1]}(y) \big)$

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