List questions from functional-equations

Published on 28 Mar 2017 - 20:28

258

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The functional equation $\frac{f(x)}{f(1-x)} = \frac{1-x}{x}$

Published on 31 Mar 2017 - 12:36

307

Views

Show that if $f(x+y)=g(x)+g(y) $ a.e. then functions are linear

Published on 01 Apr 2017 - 0:11

174

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Find a pair of analytic functions?

Published on 26 Mar 2026 - 1:28

1.2k

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Find the function f for $f$ be a function and $f(x) + f ( \frac{3x-1}{13x-4} ) = x$

Published on 03 Apr 2017 - 19:09

50

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Functions that are both Abel and Bernstein?

Published on 04 Apr 2017 - 23:03

263

Views

Iterated function derivative

Published on 05 Apr 2017 - 9:45

75

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How to prove this polynomial is a solution of this functional equation?

Published on 05 Apr 2017 - 15:24

862

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$(f(x))^2=f(2x)+2f(x)-2$ Functional Equation

Published on 05 Apr 2017 - 20:56

766

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Find all functions $f:\mathbb R \rightarrow \mathbb R$, such that: $(x^2 − y^2)\cdot f(xy) = x\cdot f(x^2y) − y\cdot f(xy^2)$

Published on 07 Apr 2017 - 8:06

265

Views

can we find actual function from $f(xy)=f(x)+f(y)$

Published on 07 Apr 2017 - 17:15

40

Views

Functional equation over reals

Published on 29 Jan 2023 - 10:46

77

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Tips for functional equations using continuity

Published on 26 Mar 2026 - 2:25

122

Views

An exercise on a function $f$ satisfying $f(x+y)=f(x)+f(y)$

Published on 14 Mar 2026 - 13:01

549

Views

Can we find an integer function satisfying these conditions?

Published on 06 Feb 2023 - 0:15

List Question

Using mean value theorem for functionals.

The functional equation $\frac{f(x)}{f(1-x)} = \frac{1-x}{x}$

Show that if $f(x+y)=g(x)+g(y) $ a.e. then functions are linear

Find a pair of analytic functions?

Find the function f for $f$ be a function and $f(x) + f ( \frac{3x-1}{13x-4} ) = x$

Functions that are both Abel and Bernstein?

Iterated function derivative

How to prove this polynomial is a solution of this functional equation?

$(f(x))^2=f(2x)+2f(x)-2$ Functional Equation

Find all functions $f:\mathbb R \rightarrow \mathbb R$, such that: $(x^2 − y^2)\cdot f(xy) = x\cdot f(x^2y) − y\cdot f(xy^2)$

can we find actual function from $f(xy)=f(x)+f(y)$

Functional equation over reals

Tips for functional equations using continuity

An exercise on a function $f$ satisfying $f(x+y)=f(x)+f(y)$

Can we find an integer function satisfying these conditions?

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