I have to add : psuedounivalent must be a uniqueness criterion but without existance proven.

This follows from the earlier proven fact that sexp(z) analytic for Re(z)>0 is already a uniqueness criterion.

Hence the question becomes : is this analytic function sexp(z) pseudounivalent ?

We know that sexp(z) has singularies. In the thread " the fermat superfunction " I noticed that most entire functions are not pseudounivalent. The follows from the nonbijective nature of most entire functions and the many amount of fixpoints/zero's of most entire functions.

This motivated me to wonder about functions that are not entire hence returning to sexp(z).

Naturally I also wonder about other superfunctions ofcourse.

I do not recall the exact location of all previous posts regarding these issues but on MSE mick made a related post.

The case which mick answer is actually about exp, but the same applies by analogue to sexp for Re(z)>0.

http://math.stackexchange.com/questions/...-equations
Btw his score of -5 is rediculous.

This reminds me of the reasons why I am not or no longer on places such as MSE , sci.math, wiki etc.

Tetration forum rules

But other tend not too imho.

regards

tommy1729