Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By hedi

Thread: help for question on bound of f(0)

  1. November 16th 2012, 03:22 AM #1
    alphabeta89
    alphabeta89 is offline
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    help for question on bound of f(0)

    Let f(z) be a function which is analytic on and inside the circle |z| = 1 and which satisfies |f(z)|\leq{M} for all z on the circle |z| = 1. Prove that |f(0)|\leq{M}.

    By Cauchy's inequality i managed to obtain
    |f'(0)|\leq{\frac{1!M}{1^1}=M}.

    How do i proceed to prove that |f(0)|\leq{M}? Any help/suggestion is welcome!
    Follow Math Help Forum on Facebook and Google+
  2. November 16th 2012, 04:07 AM #2
    FernandoRevilla
    FernandoRevilla is offline
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,154
    Thanks
    38

    Re: help for question on bound of f(0)

    Quote Originally Posted by alphabeta89 View Post
    How do i proceed to prove that |f(0)|\leq{M}? Any help/suggestion is welcome!
    Hint: 0!=1 and 1^0=1.
    Follow Math Help Forum on Facebook and Google+
  3. November 16th 2012, 04:13 AM #3
    hedi
    hedi is offline
    Member
    Joined
    Oct 2012
    From
    israel
    Posts
    77
    Thanks
    14

    Re: help for question on bound of f(0)

    use the Cauchy integral formula to evaluate and estimate f(0) as an integral over the unit circle.
    Last edited by hedi; November 16th 2012 at 04:16 AM.
    Follow Math Help Forum on Facebook and Google+
  4. November 16th 2012, 04:17 AM #4
    alphabeta89
    alphabeta89 is offline
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    Re: help for question on bound of f(0)

    Quote Originally Posted by FernandoRevilla View Post
    Hint: 0!=1 and 1^0=1.
    Hi, does Cauchy's inequality hold for |f^{(0)}(0)| in this case?
    Follow Math Help Forum on Facebook and Google+
  5. November 16th 2012, 05:04 AM #5
    hedi
    hedi is offline
    Member
    Joined
    Oct 2012
    From
    israel
    Posts
    77
    Thanks
    14

    Re: help for question on bound of f(0)

    Yes,see attached.
    Attached Thumbnails Attached Thumbnails help for question on bound of f(0)-001.jpg  
    Thanks from alphabeta89
    Follow Math Help Forum on Facebook and Google+
  6. November 16th 2012, 05:15 AM #6
    alphabeta89
    alphabeta89 is offline
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    Re: help for question on bound of f(0)

    Quote Originally Posted by hedi View Post
    Yes,see attached.
    Thanks man!
    Follow Math Help Forum on Facebook and Google+
« Can I change the base number in y=c*b^x ? | find a norm on R2 »

Similar Math Help Forum Discussions

  1. glb and lub (greatest lower bound and least upper bound)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 4th 2012, 04:30 PM
  2. Error Bound question
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 5th 2010, 09:57 PM
  3. Partial sets/ Least upper bound/Greastest lower bound/Lattices
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: February 19th 2010, 01:06 AM
  4. greatest least bound and least upper bound proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 4th 2009, 04:44 PM
  5. least upper bound and greatest lower bound
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 22nd 2007, 09:59 AM

Search Tags


/mathhelpforum @mathhelpforum