Re: f( x +2f(y) ) = f(x) + y + f(y)".
From: Alain Verghote (alainverghote_at_yahoo.fr)
Date: 01/02/05
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Date: Sun, 2 Jan 2005 16:37:22 +0000 (UTC)
On 01 Jan 2005, Stuart M Newberger wrote:
>
>Alain Verghote wrote:
>> Dear Friends,
>> I wish you all a very Happy New Year.
>>
>> Thanks for your precise and various comments.
>> You see I am trying to collect simple direct solving methods.
>> So there is a fact we may use to detect a solution f(x)=x.
>> " equal LHS and RHS occurrences of each variable (letter)".
>> I give an other exemple:
>> f(x +f(y) +f[2](x +y) )= 2x + 2y .
>
>
Dear Stuart,
>> For f[2](x +y) ; let's start from
f(u) twice iterated->f(f(u) or f^[2](u) and u=(x +y) ;
sorry I'd better written f^[2](x +y).
"the previous posts" dealt with a functional equation.
Alain.
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