Help with convex function properties

[pamparana]

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

 

[viraltux]

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

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?

 

[pamparana]

Of course. I am so stupid!

Thanks!
Luca

 

[viraltux]

Of course. I am so stupid!

Thanks!
Luca