Question

Uniqueness of solution of an integral equation [Updated]

score 454 · Answer 1 · 2026-04-11 09:57:39

454

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Uniqueness of solution of an integral equation [Updated]

Published on 11 Apr 2026 - 9:57

score 153 · Answer 2 · 2020-11-15 22:31:50

153

Views

find all polynomials that satisfy $(x-16)P(2x)=16(x-1)P(x)$

Published on 15 Nov 2020 - 22:31

score 40 · Answer 3 · 2026-04-11 21:38:14

40

Views

Question regarding the existence of a general solution to the functional equation $f \circ f = af$

Published on 11 Apr 2026 - 21:38

score 49 · Answer 4 · 2020-11-18 02:56:25

49

Views

Functional Differential Eq. $ y''(x) - A y'(x) - B y(x) + \alpha B y(\alpha x)= 0$

Published on 18 Nov 2020 - 2:56

score 1.5k · Answer 5 · 2020-11-18 07:20:29

1.5k

Views

Find $f:f(xf(x)+f(y))=f(x)^2+y$

Published on 18 Nov 2020 - 7:20

score 314 · Answer 6 · 2020-11-18 07:49:03

314

Views

Find all differentiable functions $f : [0, +\infty) \rightarrow \mathbb{R}$ such that $f(1) = 1$ and $f(x)f(y) \leq f(xy)$

Published on 18 Nov 2020 - 7:49

score 119 · Answer 7 · 2020-11-21 06:00:49

119

Views

Find $f(x)$, given $f(x+y) - 2f(x-y) + f(x) - 2f(y) = y - 2$

Published on 21 Nov 2020 - 6:00

score 76 · Answer 8 · 2026-04-09 19:46:48

76

Views

Solving a problem on differentiation

Published on 09 Apr 2026 - 19:46

score 53 · Answer 9 · 2026-03-26 14:21:15

53

Views

Uniqueness of the solution of the functional equation $ \frac{\phi(x) + \phi(y)}{2} = \phi\left(\frac{2xy}{x+y}\right) $

Published on 26 Mar 2026 - 14:21

score 68 · Answer 10 · 2020-11-23 17:51:03

68

Views

Proving that $f(x)=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{ixy}\int_{-\infty}^{\infty}e^{-ixy}f(x)dxdy$.

Published on 23 Nov 2020 - 17:51

score 84 · Answer 11 · 2026-03-29 05:44:11

84

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Is there a function of bounded variation on $[0,1]$, say $f$, such that $f(x)-2x \sqrt{V^x_0(f)}= \frac{5}{4}x^2$ for all $x \in [0,1]$?

Published on 29 Mar 2026 - 5:44

score 79 · Answer 12 · 2020-11-24 15:02:56

A functial equations problem over nonzero reals: $ f ( x y ) = f ( x ) f ( y ) $ and $ f \big( f ( x ) \big) = f ( x ) $

score 315 · Answer 13 · 2020-11-26 08:46:24

315

Views

functional equation:$f(f(x))=6x-f(x)$

Published on 26 Nov 2020 - 8:46

score 220 · Answer 14 · 2020-11-26 21:51:42

220

Views

The functional equation $f(x) + f\bigl(x+f(y)\bigr) = y + f\Bigl(f(x) + f\bigl(f(y)\bigr)\Bigr)$

Published on 26 Nov 2020 - 21:51

score 154 · Answer 15 · 2026-03-25 11:33:43

154

Views

Has there been any exploration on Cubic Power Series?

Published on 25 Mar 2026 - 11:33

List Question

Uniqueness of solution of an integral equation [Updated]

find all polynomials that satisfy $(x-16)P(2x)=16(x-1)P(x)$

Question regarding the existence of a general solution to the functional equation $f \circ f = af$

Functional Differential Eq. $ y''(x) - A y'(x) - B y(x) + \alpha B y(\alpha x)= 0$

Find $f:f(xf(x)+f(y))=f(x)^2+y$

Find all differentiable functions $f : [0, +\infty) \rightarrow \mathbb{R}$ such that $f(1) = 1$ and $f(x)f(y) \leq f(xy)$

Find $f(x)$, given $f(x+y) - 2f(x-y) + f(x) - 2f(y) = y - 2$

Solving a problem on differentiation

Uniqueness of the solution of the functional equation $ \frac{\phi(x) + \phi(y)}{2} = \phi\left(\frac{2xy}{x+y}\right) $

Proving that $f(x)=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{ixy}\int_{-\infty}^{\infty}e^{-ixy}f(x)dxdy$.

Is there a function of bounded variation on $[0,1]$, say $f$, such that $f(x)-2x \sqrt{V^x_0(f)}= \frac{5}{4}x^2$ for all $x \in [0,1]$?

A functial equations problem over nonzero reals: $ f ( x y ) = f ( x ) f ( y ) $ and $ f \big( f ( x ) \big) = f ( x ) $

functional equation:$f(f(x))=6x-f(x)$

The functional equation $f(x) + f\bigl(x+f(y)\bigr) = y + f\Bigl(f(x) + f\bigl(f(y)\bigr)\Bigr)$

Has there been any exploration on Cubic Power Series?

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