+- Tetration Forum (https://tetrationforum.org)
+-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3)
+--- Thread: final uniqueness condition ... probably (/showthread.php?tid=484)
final uniqueness condition ... probably - tommy1729 - 07/28/2010
d f^2 / d x^2 sexp(slog(x) + k) > 0 for all real x and all real k with 0 < k < Q where Q is any nonzero positive real.
assuming sexp resp slog to be C^2 of course , i 'believe' this condition implies analytic as well.
is this equivalent to d f^2 / d x^2 sexp(x) > 0 for all positive real x ?
i assume because of the substitution x = sexp(y)
sexp(slog(x) + k) = sexp(y + k) d sexp(y) ...
i believe the analogue uniqueness condition for other function as exp(x) that dont have a real fixpoint , map R to R and safisfy f ' (real) > 0 and f '' (real) > 0 to hold.
(this is an improved version of an earlier thread.)
regards
tommy1729