Results 1 to 1 of 1

Math Help - Intermediate Value Theorem for Two Dimensional Case

  1. #1
    Senior Member bkarpuz's Avatar
    Joined
    Sep 2008
    From
    R
    Posts
    481
    Thanks
    2

    Exclamation Intermediate Value Theorem for Two Dimensional Case

    Dear all, I wonder to know whether any of you have seen a result similar to that I write below.
    If so please redirect me to its proof, I just wonder to see.

    Theorem. Let f\in C([0,1]^{2},\mathbb{R}) be increasing in both of its variables and that f(0,0)<0 and f(1,1)>0.
    Then, there exists \alpha\in C([0,1],[0,1]^{2}) such that f\circ\alpha=0 on [0,1].

    Thanks.
    Last edited by bkarpuz; September 29th 2009 at 05:34 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof of intermediate value theorem for a particular case
    Posted in the Differential Geometry Forum
    Replies: 11
    Last Post: April 26th 2011, 06:37 AM
  2. Mean value theorem (multivariate case)
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 8th 2010, 11:59 AM
  3. Intermediate Value Theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2009, 08:49 AM
  4. Intermediate Value Theorem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 8th 2009, 08:19 PM
  5. intermediate value theorem/rolle's theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 8th 2007, 01:55 PM

Search Tags


/mathhelpforum @mathhelpforum