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Help with convex function properties

  1. Jun 17, 2012 #1
    Hello all,

    I am reading a paper and there is one bit in the paper that I am having a bit of trouble understanding.

    Say V(a) is a convex function and then the paper has the following line:

    [V(-2pi + a] + V(2pi + a]] >= 2V(a)

    I am sure this relationship is simple and falls out somehow from the definition of convex functions but I am unable to convince myself of it.

    I would be very grateful if someone can help me with figuring out why this relationship holds.

    Many thanks,

    Luca
     
  2. jcsd
  3. Jun 17, 2012 #2
    Hi Luca,

    Well, if given two points in a convex function you can always find another point between these two with a lower or equal value and you have V(-2pi + a) + V(2pi + a) >= 2V(a) it simply tells you that a is one of these points between -2pi+a and 2pi+a... right?
     
  4. Jun 17, 2012 #3
    Of course. I am so stupid!

    Thanks!
    Luca
     
  5. Jun 17, 2012 #4
    :wink:
     
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