final uniqueness condition ... probably - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/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