Question

Functional Equation Involving Trigonometric Functions: $f(\sin x +\sin y)=f(x+y)$

score 115 · Answer 1 · 2020-02-23 20:41:32

115

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Functional Equation Involving Trigonometric Functions: $f(\sin x +\sin y)=f(x+y)$

Published on 23 Feb 2020 - 20:41

score 368 · Answer 2 · 2020-02-24 12:05:03

368

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Find all functions such that $af(x-1)+bf(1-x)=cx$, where $a$,$b$ and $c$ are real and $a^2$ is not equal to $b^2$

Published on 24 Feb 2020 - 12:05

score 281 · Answer 3 · 2026-03-25 19:03:33

281

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$f(z) = z + f(z^2)$ outside the unit disk?

Published on 25 Mar 2026 - 19:03

score 313 · Answer 4 · 2026-03-25 14:00:36

313

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Need help solving a min-max fixed point equation

Published on 25 Mar 2026 - 14:00

score 33 · Answer 5 · 2020-03-04 03:36:32

33

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Does fixed point iteration converges in a second type Fredhom Equation?

Published on 04 Mar 2020 - 3:36

score 634 · Answer 6 · 2026-03-29 19:14:33

634

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IMO 2019: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(2a) + 2\, f(b) = f \big( f (a+b)\big)$.

Published on 29 Mar 2026 - 19:14

score 94 · Answer 7 · 2020-03-05 10:42:01

94

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If $f\big(f(x)\big)=2^x-1$ for every $x\in\mathbb{R}$, then what is $f(0)+f(1)$?

Published on 05 Mar 2020 - 10:42

score 164 · Answer 8 · 2020-03-06 09:19:19

Functional equation in one variable: $f(x)=\frac{1}{4}f(2x)+\frac{1}{4}f\left(\frac{x}{3}\right)+\frac{1}{2}f\left(\frac{x}{5}\right)$

score 109 · Answer 9 · 2020-03-10 18:08:52

109

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A problem regarding the conjugacy classes of homeomorphism group .

Published on 10 Mar 2020 - 18:08

score 38 · Answer 10 · 2026-03-26 17:52:09

38

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Question on variable change in functional

Published on 26 Mar 2026 - 17:52

score 51 · Answer 11 · 2020-03-12 15:47:37

51

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Taylor Series Approximations for Functional Equations

Published on 12 Mar 2020 - 15:47

score 76 · Answer 12 · 2020-03-13 04:00:07

76

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Functional equation, $f(x) f(y) = f(x + y) + xy$

Published on 13 Mar 2020 - 4:00

score 110 · Answer 13 · 2026-03-27 13:46:07

110

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Means defined by tangent parallel to secant

Published on 27 Mar 2026 - 13:46

score 95 · Answer 14 · 2020-03-15 18:13:15

95

Views

Solving for polynomial $f(x)$ satisfying $f(x)f(y)=f(x)+f(y)+f(xy)-2 \forall x\in \mathbb{R}, f(1)\ne 1, f(3)=10$

Published on 15 Mar 2020 - 18:13

score 46 · Answer 15 · 2020-03-16 13:45:50

46

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Solve this equation: $\frac{f(x)}{\int_{0}^{x_1} f(x)dx}=\frac{g(x)}{\int_{0}^{x_1} g(x)dx}$

Published on 16 Mar 2020 - 13:45

List Question

Functional Equation Involving Trigonometric Functions: $f(\sin x +\sin y)=f(x+y)$

Find all functions such that $af(x-1)+bf(1-x)=cx$, where $a$,$b$ and $c$ are real and $a^2$ is not equal to $b^2$

$f(z) = z + f(z^2)$ outside the unit disk?

Need help solving a min-max fixed point equation

Does fixed point iteration converges in a second type Fredhom Equation?

IMO 2019: Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(2a) + 2\, f(b) = f \big( f (a+b)\big)$.

If $f\big(f(x)\big)=2^x-1$ for every $x\in\mathbb{R}$, then what is $f(0)+f(1)$?

Functional equation in one variable: $f(x)=\frac{1}{4}f(2x)+\frac{1}{4}f\left(\frac{x}{3}\right)+\frac{1}{2}f\left(\frac{x}{5}\right)$

A problem regarding the conjugacy classes of homeomorphism group .

Question on variable change in functional

Taylor Series Approximations for Functional Equations

Functional equation, $f(x) f(y) = f(x + y) + xy$

Means defined by tangent parallel to secant

Solving for polynomial $f(x)$ satisfying $f(x)f(y)=f(x)+f(y)+f(xy)-2 \forall x\in \mathbb{R}, f(1)\ne 1, f(3)=10$

Solve this equation: $\frac{f(x)}{\int_{0}^{x_1} f(x)dx}=\frac{g(x)}{\int_{0}^{x_1} g(x)dx}$

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