List questions from functional-equations

Published on 07 May 2026 - 10:10

289

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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 29 Apr 2026 - 12:18

135

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Easy looking functional equation.

Published on 10 May 2026 - 8:02

125

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Constructing a functional equation that has given solution set.

Published on 07 May 2026 - 18:18

117

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

Published on 07 May 2026 - 13:01

147

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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 05 May 2026 - 2:44

180

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Stationary Condition of Variational Iteration Method

Published on 03 May 2026 - 4:58

765

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

Published on 07 May 2026 - 15:02

95

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

Published on 02 May 2026 - 18:21

84

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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 29 Apr 2026 - 12:18

77

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Functiοnal Εquation in Real Line

Published on 07 May 2026 - 20:05

159

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

Published on 29 Apr 2026 - 12:19

1.3k

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

Published on 29 Apr 2026 - 12:19

160

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

Published on 01 May 2026 - 15:47

108

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

Published on 02 May 2026 - 5:16

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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