Help with convex function properties

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Discussion Overview

The discussion revolves around the properties of convex functions, specifically examining a relationship involving a convex function V(a) and its values at certain points. The focus is on understanding why the inequality V(-2pi + a) + V(2pi + a) >= 2V(a) holds true, as presented in a paper.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Luca expresses confusion regarding the inequality related to convex functions and seeks clarification on its validity.
  • Another participant suggests that the inequality indicates that the point a lies between the points -2pi + a and 2pi + a, which is a characteristic of convex functions.

Areas of Agreement / Disagreement

Participants appear to agree on the general properties of convex functions, but the discussion does not reach a consensus on the specific reasoning behind the inequality.

Contextual Notes

Participants do not provide detailed mathematical justifications or definitions, leaving some assumptions and steps unresolved.

pamparana
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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
 
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pamparana said:
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?
 
Of course. I am so stupid!

Thanks!
Luca
 
pamparana said:
Of course. I am so stupid!

Thanks!
Luca

:wink:
 

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