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Math Help - convex function

  1. #1
    Junior Member
    Joined
    Sep 2007
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    66

    Wink convex function

    If f is continuous function on (a,b)is convex,show that
    for x_{1},x_{2},....,x_{m}\in(a,b),
    that

    f(\frac{x_{1}+x_{2}+...+x_{m}}{m})\leq\frac{1}{m}(  f(x_{1})+f(x_{2})+...+f(x_{m}))


    thanks very much
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  2. #2
    Super Member PaulRS's Avatar
    Joined
    Oct 2007
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    That's a particular case of Jensen's Inequality

    Here's a proof I particularly enjoyed reading Art of Problem Solving Forum

    And here you have the traditional proof: http://en.wikipedia.org/wiki/Jensen's_inequality

    It's a very useful inequality.
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