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On 30.09.2006 11:50, alainverghote@xxxxxxxx wrote:
> theronruiz@xxxxxxxxxxx a écrit :
>
>> S is the set of all R -> R functions.
>> T is a S -> S function such that:
>>
>> T(f o g) = (T(f) o g) * T(g) for every f and g in S,
>> where (f o g)(x) = f(g(x)) and (f * g)(x) = f(x) * g(x).
>>
>> Are there non-constant solutions?
>>
>> Thank you,
>> Theron
>
> Bonjour ,
> I do not understand your writing :
> what does T(f) mean in ( T(f) o g ) ?
My understanding of this notation is that it is a composition of the map
T(f) and g, i.e. (T(f) o g)(x) = T(f)(g(x)).
> T o f ; idem for T(g) .
> Are you interested in fonctional equations like
> T(g(f(x))) = T(f(x)) * T(g(x)) in R
> or g(f(x)) = f(x) * g(x) ?
> tell us which are the unknown functions ,
>
> Alain
>
J.
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