Question

Olympiad functional equations proof verification: $f\bigl(2f(x)+f(y)\bigr)=2x+y$ on $\mathbb Q$ and $f\bigl(xf(x)+f(y)\bigr)=f(x)^2+y$ on $\mathbb R$

score 127 · Answer 1 · 2021-01-26 10:45:35

127

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Olympiad functional equations proof verification: $f\bigl(2f(x)+f(y)\bigr)=2x+y$ on $\mathbb Q$ and $f\bigl(xf(x)+f(y)\bigr)=f(x)^2+y$ on $\mathbb R$

Published on 26 Jan 2021 - 10:45

score 56 · Answer 2 · 2026-04-07 21:12:09

56

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Solving a bivariate recursion $f(k, n) = n^m f(k-n, m)$

Published on 07 Apr 2026 - 21:12

score 169 · Answer 3 · 2026-04-13 09:23:22

169

Views

A function with period 1 and $\alpha$ (irrational)

Published on 13 Apr 2026 - 9:23

score 127 · Answer 4 · 2026-04-11 02:56:54

127

Views

Laplace transform of solution of an integral equation for non-recursive logistic map computations

Published on 11 Apr 2026 - 2:56

score 56 · Answer 5 · 2026-04-11 13:12:40

56

Views

Dropping continuity condition on functional equation

Published on 11 Apr 2026 - 13:12

score 43 · Answer 6 · 2026-04-12 12:48:56

43

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See if this functional equation works for some function and write down the domain and co-domain

Published on 12 Apr 2026 - 12:48

score 320 · Answer 7 · 2026-04-13 05:18:12

320

Views

Chain rule for functional derivates with the same variables

Published on 13 Apr 2026 - 5:18

score 51 · Answer 8 · 2026-04-11 15:50:44

51

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Golden functions?

Published on 11 Apr 2026 - 15:50

score 267 · Answer 9 · 2026-04-12 02:34:46

267

Views

Differential equation with one univariate function and several variables

Published on 12 Apr 2026 - 2:34

score 208 · Answer 10 · 2021-02-15 17:38:45

208

Views

Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $f(x^2 + y + f(y)) = 2y + (f(x))^2$

Published on 15 Feb 2021 - 17:38

score 83 · Answer 11 · 2026-04-13 03:50:16

83

Views

Solution of a functional equation $f(x+y)=f_1(x)+f_2(y)$

Published on 13 Apr 2026 - 3:50

score 60 · Answer 12 · 2026-04-13 01:42:36

60

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How many functions $f\colon A\to B$ with the following property: $f (x + y) = f (x) + f (y)$ for every $x, y\in A$

Published on 13 Apr 2026 - 1:42

score 162 · Answer 13 · 2021-02-25 03:44:43

162

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Find all functions $f:\mathbb N\to\mathbb N$ such that $f\left(f(m)+f(n)\right)=m+n$, for all $m,n \in\mathbb N$.

Published on 25 Feb 2021 - 3:44

score 142 · Answer 14 · 2021-02-26 12:43:56

142

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Find all fucntions such that $f:\Bbb R \to \Bbb R$ and $f(x^{2}+yf(x))=f(x+y)$

Published on 26 Feb 2021 - 12:43

score 59 · Answer 15 · 2026-04-12 22:58:13

59

Views

Dependance of variables in variational calculus

Published on 12 Apr 2026 - 22:58

List Question

Olympiad functional equations proof verification: $f\bigl(2f(x)+f(y)\bigr)=2x+y$ on $\mathbb Q$ and $f\bigl(xf(x)+f(y)\bigr)=f(x)^2+y$ on $\mathbb R$

Solving a bivariate recursion $f(k, n) = n^m f(k-n, m)$

A function with period 1 and $\alpha$ (irrational)

Laplace transform of solution of an integral equation for non-recursive logistic map computations

Dropping continuity condition on functional equation

See if this functional equation works for some function and write down the domain and co-domain

Chain rule for functional derivates with the same variables

Golden functions?

Differential equation with one univariate function and several variables

Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $f(x^2 + y + f(y)) = 2y + (f(x))^2$

Solution of a functional equation $f(x+y)=f_1(x)+f_2(y)$

How many functions $f\colon A\to B$ with the following property: $f (x + y) = f (x) + f (y)$ for every $x, y\in A$

Find all functions $f:\mathbb N\to\mathbb N$ such that $f\left(f(m)+f(n)\right)=m+n$, for all $m,n \in\mathbb N$.

Find all fucntions such that $f:\Bbb R \to \Bbb R$ and $f(x^{2}+yf(x))=f(x+y)$

Dependance of variables in variational calculus

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