# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 25 May 2013 14:09:08 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 7 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Modulus and complex variablePosted: Mon, 6 Feb 2012 06:24:33 UTC
 Member

Joined: Mon, 6 Feb 2012 06:18:16 UTC
Posts: 25
Let be an analytic function so that Prove that for all is

No clue on this one, any ideas? I thought on considering or perhaps but I don't see the trick to solve the problem.

Top

 Post subject: Re: Modulus and complex variablePosted: Mon, 6 Feb 2012 06:29:39 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6009
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
LegendZKiller wrote:
Let be an analytic function so that Prove that for all is

No clue on this one, any ideas? I thought on considering or perhaps but I don't see the trick to solve the problem.

Schwarz-Pick.

_________________

Top

 Post subject: Re: Modulus and complex variablePosted: Mon, 6 Feb 2012 13:19:36 UTC
 Member

Joined: Mon, 6 Feb 2012 06:18:16 UTC
Posts: 25
I don't get how to apply it, can you show me please?

Top

 Post subject: Re: Modulus and complex variablePosted: Mon, 6 Feb 2012 14:50:33 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
LegendZKiller wrote:
I don't get how to apply it, can you show me please?

Huh? You know the center and radius of the ball you're working on, where's the problem?

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Modulus and complex variablePosted: Tue, 7 Feb 2012 02:37:49 UTC
 Member

Joined: Mon, 6 Feb 2012 06:18:16 UTC
Posts: 25
I don't see the trick, I suppose to take a function, for example something like that, and having the ball I have that right?

Top

 Post subject: Re: Modulus and complex variablePosted: Tue, 7 Feb 2012 02:39:16 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
LegendZKiller wrote:
I don't see the trick, I suppose to take a function, for example something like that, and having the ball I have that right?

What? Do you know the Schwarz-Pick theorem?

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Modulus and complex variablePosted: Tue, 7 Feb 2012 03:12:12 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6009
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Oops...

Are you sure the denominator of LHS of the desired inequality is not ? For that you need to assume in addition (which also has the effect of replacing the with except at z=1).

_________________

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 7 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous