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From: Patrick Coilland on 2 Feb 2010 04:09
Patrick Coilland a �crit :
>
> There are no solution if you add the constraint f(x)>0 since for example
> f(f(-1))=-1<0
>
Little mistake here : there are no solution for f(x)>0 forall x since
f(f(-1))=-f(f(1))
From: Alfred Flaßhaar on 2 Feb 2010 05:54
Patrick Coilland wrote:
> Patrick Coilland a �crit :
>>
>> There are no solution if you add the constraint f(x)>0 since for
>> example f(f(-1))=-1<0
>>
> Little mistake here : there are no solution for f(x)>0 forall x since
> f(f(-1))=-f(f(1))

Thank You, that helps.

Alfred

From: Tim Little on 2 Feb 2010 19:38
On 2010-02-01, Dan Cass <dcass(a)sjfc.edu> wrote:
>> f(f(x))/x = f(f(y))/y (*)
>
> There may be (probably are) solutions for which neither side of (*)
> is constant.

Let y = c for some constant c, and k = f(f(c))/c. Then f(f(x))/x = k
for all x.

The case k = 1 implies that f is an involution, and another
interesting case is k = 0 which does have some nontrivial solutions.


- Tim
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