List questions from functional-equations

Published on 03 Aug 2010 - 0:13

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Function Satisfying $f(x)=f(2x+1)$

Published on 12 Aug 2010 - 10:36

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Continuous function satisfying $f^{k}(x)=f(x^k)$

Published on 13 Aug 2010 - 13:33

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On the functional square root of $x^2+1$

Published on 31 Mar 2026 - 6:00

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Polynomials which satisfy $p^{2}(x)-1 = p(x^{2}+1)$

Published on 01 Sep 2010 - 8:51

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Find polynomials such that $(x-16)p(2x)=16(x-1)p(x)$

Published on 02 Sep 2010 - 17:57

254

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How to solve DE that relate values of derivatives at different points?

Published on 04 Sep 2010 - 17:04

3.5k

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Solving the functional Equation $f(f(x))=f(x)+x$

Published on 06 Sep 2010 - 21:50

1.8k

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Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$

Published on 09 Sep 2010 - 19:21

249

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Finding $\alpha$ such that $f(\alpha(x+y))=f(x)+f(y)$

Published on 11 Sep 2010 - 19:49

461

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Solving $f(f(x))=g(x)$ equations

Published on 19 Sep 2010 - 16:21

369

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Implicit function $y = e^{(y-1)/x}$

Published on 01 Oct 2010 - 18:49

256

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Generalization of cos: is this function known?

Published on 29 Oct 2010 - 20:49

218

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Solving this set of quadratic equations

Published on 04 Nov 2010 - 20:32

742

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Find all continuous functions $f$ on $\mathbb{R}$ satisfying $f(x)=f(\sin x)$ for all $x$.

Published on 11 Nov 2010 - 23:22

List Question

Prove that this function is bounded

Function Satisfying $f(x)=f(2x+1)$

Continuous function satisfying $f^{k}(x)=f(x^k)$

On the functional square root of $x^2+1$

Polynomials which satisfy $p^{2}(x)-1 = p(x^{2}+1)$

Find polynomials such that $(x-16)p(2x)=16(x-1)p(x)$

How to solve DE that relate values of derivatives at different points?

Solving the functional Equation $f(f(x))=f(x)+x$

Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$

Finding $\alpha$ such that $f(\alpha(x+y))=f(x)+f(y)$

Solving $f(f(x))=g(x)$ equations

Implicit function $y = e^{(y-1)/x}$

Generalization of cos: is this function known?

Solving this set of quadratic equations

Find all continuous functions $f$ on $\mathbb{R}$ satisfying $f(x)=f(\sin x)$ for all $x$.

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