List questions from functional-equations

Published on 16 Dec 2016 - 4:10

393

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Prove or disprove that $f$ is identity function given that $f$ is continuous and $f(f(f(x)))=x$

Published on 16 Dec 2016 - 7:01

465

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Prove that $\frac{a}{2}x^2+bx+c=0$ has a root between $x_1$ and $x_2$.

Published on 17 Dec 2016 - 5:43

176

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Finding the functions $f : \Bbb N \to \Bbb N$ which satisfy $f\circ f(x) + f(x) = 2x+15$

Published on 19 Dec 2016 - 15:12

1.5k

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Is a cone in Banach space always a closed subset?

Published on 19 Dec 2016 - 23:42

264

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Finding $f(x)$ from a equation

Published on 20 Dec 2016 - 6:09

75

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A functional equation in two variables

Published on 21 Dec 2016 - 14:08

131

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$f(z)$ entire function satisfying $f(z_{1} + {z_{2}})=f(z_{1})+f(z_{2})$.

Published on 22 Dec 2016 - 9:22

142

Views

Finding functions such that $f(g(x)) = f(x)g(x)$

Published on 23 Dec 2016 - 7:56

161

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Solution of $f(3x)=\frac{f(x)f(4x)}{2f(2x)}+\frac{f^2(2x)}{2f(x)}$?

Published on 24 Dec 2016 - 12:26

708

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When is a function of a product the product of functions?

Published on 25 Dec 2016 - 5:54

188

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A problem on polynomials (functional equation)

Published on 27 Dec 2016 - 15:23

83

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Surjections from $ \mathbb N $ to itself where each image has an infinity of antecedents in $ \mathbb N $

Published on 28 Dec 2016 - 12:46

35

Views

Quick way to show that the n-th composite function for a $x$ given will be equal to $0$

Published on 28 Dec 2016 - 13:02

571

Views

Functional equation $(x + y)f(f(x)y) = x^2 f(f(x) + f(y))$

Published on 29 Dec 2016 - 14:43

List Question

If $f(f(x)) = -x$ then is $f$ continuous?

Prove or disprove that $f$ is identity function given that $f$ is continuous and $f(f(f(x)))=x$

Prove that $\frac{a}{2}x^2+bx+c=0$ has a root between $x_1$ and $x_2$.

Finding the functions $f : \Bbb N \to \Bbb N$ which satisfy $f\circ f(x) + f(x) = 2x+15$

Is a cone in Banach space always a closed subset?

Finding $f(x)$ from a equation

A functional equation in two variables

$f(z)$ entire function satisfying $f(z_{1} + {z_{2}})=f(z_{1})+f(z_{2})$.

Finding functions such that $f(g(x)) = f(x)g(x)$

Solution of $f(3x)=\frac{f(x)f(4x)}{2f(2x)}+\frac{f^2(2x)}{2f(x)}$?

When is a function of a product the product of functions?

A problem on polynomials (functional equation)

Surjections from $ \mathbb N $ to itself where each image has an infinity of antecedents in $ \mathbb N $

Quick way to show that the n-th composite function for a $x$ given will be equal to $0$

Functional equation $(x + y)f(f(x)y) = x^2 f(f(x) + f(y))$

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