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 introducing TPID 16 tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 06/07/2014, 11:03 PM (This post was last modified: 06/18/2014, 11:37 PM by tommy1729.) 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 « Next Oldest | Next Newest »

 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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