introducing TPID 16
#1
TPID 16

Let \( f(z) \) be a nonpolynomial real entire function.
\( f(z) \) has a conjugate primary fixpoint pair : \( L + M i , L - M i. \)
\( f(z) \) has no other primary fixpoints then the conjugate primary fixpoint pair.
For \( t \) between \( 0 \) and \( 1 \) and \( z \) such that \( Re(z) > 1 + L^2 \) we have that
\( f^{[t]}(z) \) is analytic in \( z \).
\( f^{[t]}(x) \) is analytic for all real \( x > 0 \) and all real \( t \ge 0 \) .
If \( f^{[t]}(x) \) is analytic for \( x = 0 \) then :
\( \frac{d^n}{dx^n} f^{[t]}(x) \ge 0 \) for all real \( x \ge 0 \) , all real \( t \ge 0 \) and all integer \( n > 0 \).
Otherwise
\( \frac{d^n}{dx^n} f^{[t]}(x) \ge 0 \) for all real \( x > 0 \) , all real \( t \ge 0 \) and all integer \( n > 0 \).


Are there solutions for \( f(z) \) ?
I conjecture yes.


regards

tommy1729


Messages In This Thread
introducing TPID 16 - by tommy1729 - 06/07/2014, 11:03 PM
RE: introducing TPID 16 - by sheldonison - 06/08/2014, 04:05 PM
RE: introducing TPID 16 - by tommy1729 - 06/09/2014, 09:55 AM
RE: introducing TPID 16 - by tommy1729 - 06/18/2014, 11:36 PM
RE: introducing TPID 16 - by tommy1729 - 06/18/2014, 11:46 PM

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