Re: A Functional Equation
From: Alain Verghote (alainverghote_at_yahoo.fr)
Date: 08/19/04
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Date: 19 Aug 2004 11:45:00 -0400
On 18 Aug 2004 16:45:01 -0400, Mikhail V. Sokolov wrote:
>What can be said about the function F(x,y) if it admits the following
>properties:
>1. F(x,x)=0 for all x;
>2. F(x,y) is strictly decreasing and continuous in the second
variable
>y for each choice of the first variable x;
>3. For any fixed reals x[1],...,x[n] if x is a unique solution of the
>equation F(x[1],x)+...+F(x[n],x)=0 then as well
>F(x[1]+A,x+A)+...+F(x[n]+A,x+A)=0 for any real A.
>
>Thank you very much for any advance, Mikhail.
Dear Mikhail,
I've proposed an iterated solution on sci.math
f(x,y)= m^[x-y](c)-c or m^[x]o m^[-y](c)-c :
[x-y],[x],[-y] iterations of function m.
For instance (2*c)^[x-y]-c or c*2^(x-y)-c .
Alain.
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