List questions from functional-equations

Published on 22 Mar 2026 - 4:24

282

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How to solve the integral equation $f(x) = \int_0^x f(x-y)k(x,y)dy+g(x)$ for $f(x)$?

Published on 20 Mar 2026 - 9:02

123

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Easy looking functional equation.

Published on 22 Mar 2026 - 11:03

117

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Constructing a functional equation that has given solution set.

Published on 19 Mar 2026 - 20:35

108

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Solution of $f(ax+b)=kf(x)$ with $k,a,b$ are real numbers

Published on 22 Mar 2026 - 10:23

141

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Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization

Published on 17 Mar 2026 - 9:08

171

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Stationary Condition of Variational Iteration Method

Published on 22 Mar 2026 - 9:15

757

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How to solve the functional equation $f(x + f(x +y ) ) = f(2x) + y$?

Published on 20 Mar 2026 - 1:05

85

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Solution to the functional equation $f(z)=(-1)^zf(1-z)$???

Published on 20 Mar 2026 - 7:32

79

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If $f(a,b)=f(a,c)f(c,b)$ for all $a,b,c$, when can we conclude $f(a,b)=g(a)/g(b)$ for some $g$?

Published on 19 Mar 2026 - 21:14

67

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Functiοnal Εquation in Real Line

Published on 19 Mar 2026 - 22:06

149

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Solving $f(f(x))=2x+1$ for $f$

Published on 17 Mar 2026 - 16:22

1.2k

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Solution of a function equation $f(x) + f(y) = f(x + y + 2f(xy))$

Published on 17 Mar 2026 - 4:34

149

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Find $f(x)$ if $f\left(\frac{x+y}{3}\right)=\frac{2+f(x)+f(y)}{3}$

Published on 17 Mar 2026 - 1:29

97

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When can one write $f(x,y)$ as $|g(x)-g(y)|_2^2$ for some $g(\cdot)$?

Published on 17 Mar 2026 - 6:40

List Question

Functional equation $2f\left(\frac{x+y}{2}\right)-f(y)=f''(x)$

How to solve the integral equation $f(x) = \int_0^x f(x-y)k(x,y)dy+g(x)$ for $f(x)$?

Easy looking functional equation.

Constructing a functional equation that has given solution set.

Solution of $f(ax+b)=kf(x)$ with $k,a,b$ are real numbers

Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization

Stationary Condition of Variational Iteration Method

How to solve the functional equation $f(x + f(x +y ) ) = f(2x) + y$?

Solution to the functional equation $f(z)=(-1)^zf(1-z)$???

If $f(a,b)=f(a,c)f(c,b)$ for all $a,b,c$, when can we conclude $f(a,b)=g(a)/g(b)$ for some $g$?

Functiοnal Εquation in Real Line

Solving $f(f(x))=2x+1$ for $f$

Solution of a function equation $f(x) + f(y) = f(x + y + 2f(xy))$

Find $f(x)$ if $f\left(\frac{x+y}{3}\right)=\frac{2+f(x)+f(y)}{3}$

When can one write $f(x,y)$ as $|g(x)-g(y)|_2^2$ for some $g(\cdot)$?

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