just another uniqueness musing
#5
tommy1729 Wrote:in fact it shows the following important result :

if f(x) ( being f(f(x)) = exp(x) ) exists and is unique on a finite (real) interval I ,

then f(x) exists and is unique for all real x.

that interval I has to be large enough though.

it has to 'connect' two rectangles.

however perhaps someone can get rid of that restriction and arrive at " any finite interval " ?

regards

tommy1729
Reply


Messages In This Thread
just another uniqueness musing - by Gottfried - 02/11/2009, 12:23 PM
RE: just another uniqueness musing - by bo198214 - 02/11/2009, 03:14 PM
RE: just another uniqueness musing - by tommy1729 - 02/11/2009, 03:42 PM
RE: just another uniqueness musing - by tommy1729 - 02/11/2009, 03:50 PM
RE: just another uniqueness musing - by Gottfried - 02/11/2009, 03:48 PM
RE: just another uniqueness musing - by bo198214 - 02/12/2009, 12:10 AM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Uniqueness of fractionally iterated functions Daniel 7 11,177 07/05/2022, 01:21 AM
Last Post: JmsNxn
  Universal uniqueness criterion? bo198214 57 174,849 06/28/2022, 12:00 AM
Last Post: JmsNxn
  A question concerning uniqueness JmsNxn 4 17,008 06/10/2022, 08:45 AM
Last Post: Catullus
  [Exercise] A deal of Uniqueness-critrion:Gamma-functionas iteration Gottfried 6 15,761 03/19/2021, 01:25 PM
Last Post: tommy1729
  A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 40,625 02/17/2017, 05:21 AM
Last Post: JmsNxn
  Uniqueness of half-iterate of exp(x) ? tommy1729 14 53,380 01/09/2017, 02:41 AM
Last Post: Gottfried
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 5,749 03/19/2016, 10:44 AM
Last Post: fivexthethird
  [2014] Uniqueness of periodic superfunction tommy1729 0 6,484 11/09/2014, 10:20 PM
Last Post: tommy1729
  almost periodic musing tommy1729 1 7,360 06/17/2014, 12:24 PM
Last Post: tommy1729
  Real-analytic tetration uniqueness criterion? mike3 25 69,796 06/15/2014, 10:17 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)