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Math Help - Show that f is convex on an interval

  1. #1
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    Show that f is convex on an interval

    Hi there,
    this is one of those problems I can't even figure out how to approach. Any idea would be highly appreciated.

    Prove that
    f is convex on an interval iff for all x and y in the interval,
    f(tx + (1 t)y) < tf(x) + (1 t)f(y), for 0 < t < 1
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  2. #2
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    Quote Originally Posted by dgmath View Post
    Hi there,
    this is one of those problems I can't even figure out how to approach. Any idea would be highly appreciated.


    Prove that
    f is convex on an interval iff for all x and y in the interval,
    f(tx + (1 t)y) < tf(x) + (1 t)f(y), for 0 < t < 1



    As far as I am concerned this is exactly the definition of (upwards) convexity...which definition do you have?

    Tonio
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tonio View Post
    As far as I am concerned this is exactly the definition of (upwards) convexity...which definition do you have?

    Tonio
    [/left]
    I almost guarantee based on dgmath's previous posts that his definition is that f''(x)>0. Of course, he/she missing some extra stipulations...differentiability etc.
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  4. #4
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    Hi there,
    I guess for the same reason, I'm stuck here. what I posted is pretty much all I have, but it IS true that it is a rephrased version of definition of convexity.
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