Results 1 to 2 of 2

Math Help - Equicontinuous

  1. #1
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093

    Equicontinuous

    Prove or disprove
    F_n(x) = \sin nx is equicontinuous

    I know the definition of equicontinuous at x_0 it says for all \epsilon >0 there exist \delta>0 such that if d ( f(x_0),f(x) ) < \epsilon then
    d(x_0 , x) < \delta

    trying if it is equicontinuous at x_0 = 0
    Given \epsilon > 0

    | f(x)  | < \epsilon \Rightarrow |\sin n x | < \epsilon
    delta depends on epsilon and x just how i can continue

    any hints or any directions
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Equicontinuous

    Do we have to decide whether the family is equi-continuous at each point, or to determine the point on which the family is equi-continuous? For the first question, look at F_n\left(\frac{\pi}{2n}\right).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sup of equicontinuous is continuous
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 4th 2012, 11:29 PM
  2. if family equicontinuous, prove lipschitz
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 4th 2010, 07:18 AM
  3. Replies: 1
    Last Post: April 20th 2010, 12:40 PM
  4. equicontinuous and uniformly equicontinuous
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 6th 2006, 02:25 PM

Search Tags


/mathhelpforum @mathhelpforum