delicate multivariate functional equation puzzle 4 U
- From: "double d" <markdemers15@xxxxxxxxxxx>
- Date: 6 May 2005 21:00:57 -0700
Let x and y be real numbers, and let F(x,y,s,t) be a real-valued
function on (x,y,s,t). Double D needs to characterize (or identify)
all functions F that satisfy the following functional condition:
F(x,y) = F(x+a*z, y-(1-a)*z, s-(1-a)*a*z, t-(1-a)*a*a*z)
where:
a is some real constant with a fixed value between 0 and 1 (e.g.,
a=0.383);
z is any real number (that is, the functional equation must
simultaneously hold for ANY value of z).
What does the most general function F(x,y,s,t) satisfying such an
equation look like? Can you give
some non-trivial (non-linear) functions that solve it? [Double D
already knows the linear solution.]
Double D (math editor of equityvalue Google group)
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=667781#PaperDownload
.
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