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Hello,
I would appreciate if someone could help me on solving the following
system, or at least a proof on existence/nonexistence of solution for
it.
Definitions:
f(x,y)=sum(ak*(x^pk)*(y^qk)) k=1,...N
x and y belong to the closed interval [L,U] (where U>L)
ak,L,U belong to R+ (R+ being non-negative real numbers)
pk,qk belong to R (R being real numbers)
Main Inequality:
For ANY x in [L,U] and ANY y in [L,U]...
y<x must imply that df/dx<0 and otherwise (i.e. when y>x) df/dx>0
Is there any choice of L, U, a1,...aN, p1,...pN, q1...qN that
satisfies the constraints in this problem? If so, what is the most
general solution like? If the solution is too hard to attain, an
existence/nonexistence proof will be helpful too.
Thank you very much
H.M. |
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