open problems survey

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open problems survey

tommy1729 $Offline$
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#18

06/07/2014, 10:44 PM (This post was last modified: 06/18/2014, 11:48 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

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Messages In This Thread

open problems survey - by bo198214 - 05/17/2008, 10:03 AM

eigenvalues of Carleman matrix for b^x, TPID 1 - by bo198214 - 05/17/2008, 10:23 AM

Exponential Factorial, TPID 2 - by andydude - 05/26/2008, 03:24 PM

eigenvalues of Carleman matrix for (x+s)^p-s, TPID 3 - by bo198214 - 06/29/2008, 12:36 PM

Existence of bounded b^z TPID 4 - by bo198214 - 10/08/2008, 04:22 PM

sqrt(2) tetrational is completely discontinuous TPID 5 - by bo198214 - 05/01/2009, 09:20 AM

Limit of self-super-roots is e^1/e. TPID 6 - by andydude - 10/07/2009, 12:03 AM

A conjecture on bounds. TPID 7 - by andydude - 10/23/2009, 05:27 AM

Elementary superfunction of polynomial without real fixed points TPID 8 - by bo198214 - 04/25/2010, 10:53 AM

Logarithm reciprocal TPID 9 - by bo198214 - 07/20/2010, 05:50 AM

Convergence of Eulers and Etas. TPID 10 - by dantheman163 - 10/31/2010, 07:13 PM

RE: open problems survey - by nuninho1980 - 10/31/2010, 09:50 PM

Tommy's conjecture about Eulers and Etas. TPID 11. - by tommy1729 - 12/01/2010, 03:56 PM

convergence of self-tetra-root polynomial interpolation. TPID 12 - by bo198214 - 05/31/2011, 04:54 PM

convergence of self-root polynomial interpolation. TPID 13 - by bo198214 - 05/31/2011, 07:02 PM

Tommy's conjecture about andrew slog method. TPID 14 - by tommy1729 - 06/01/2011, 06:23 PM

Tommy's conjecture TPID 16 - by tommy1729 - 06/07/2014, 10:44 PM

Error terms for fake function theory TPID 17 - by tommy1729 - 03/28/2015, 10:48 PM

The third super-root TPID 18 - by andydude - 12/25/2015, 06:16 AM

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