12/12/2009, 12:54 AM
let f(x) be Coo.
f(f(x)) = exp(x) + x
what is f(x) ?
does the (only) fixpoint at - oo help ?
can f(x) be entire ?
is there a solution f(x) such that f(x) has no fixpoint apart from - oo ?
can f(x) be expressed in terms of tetration ?
is there a solution f(f(x)) = exp(x) + x with f(x) E Coo , f(x) mapping all reals to reals and f(x) having no fixpoint apart from - oo ?
does " a solution f(f(x)) = exp(x) + x with f(x) E Coo , f(x) mapping all reals to reals and f(x) having no fixpoint apart from - oo " imply that all derivatives are strictly positive reals ?
can f(x) be expressed in terms of pentation ?
does the substitution y = 1/x help ?
( trying to 'move the fixpoint' but problems occur e.g. exp(1/x) has a singularity at 0 ! ... on the other hand perhaps considering a certain angle towards the singularity it might work to give a real-analytic solution ? )
does the strategy lim n-> oo f(f(x)) = exp(x) + x + 1/n work ?
how about the carleman matrix method ?
this seems like a difficult problem ...
regards
tommy1729
f(f(x)) = exp(x) + x
what is f(x) ?
does the (only) fixpoint at - oo help ?
can f(x) be entire ?
is there a solution f(x) such that f(x) has no fixpoint apart from - oo ?
can f(x) be expressed in terms of tetration ?
is there a solution f(f(x)) = exp(x) + x with f(x) E Coo , f(x) mapping all reals to reals and f(x) having no fixpoint apart from - oo ?
does " a solution f(f(x)) = exp(x) + x with f(x) E Coo , f(x) mapping all reals to reals and f(x) having no fixpoint apart from - oo " imply that all derivatives are strictly positive reals ?
can f(x) be expressed in terms of pentation ?
does the substitution y = 1/x help ?
( trying to 'move the fixpoint' but problems occur e.g. exp(1/x) has a singularity at 0 ! ... on the other hand perhaps considering a certain angle towards the singularity it might work to give a real-analytic solution ? )
does the strategy lim n-> oo f(f(x)) = exp(x) + x + 1/n work ?
how about the carleman matrix method ?
this seems like a difficult problem ...
regards
tommy1729