What is the theorem that log-convexity implies convexity?

[mertcan]

Hi, in this link https://math.stackexchange.com/questions/2605752/proof-log-convex-implies-convexity , there is a theorem that labelled with yellow. I do not know the name of theorem and would like to know it's derivation. Could you please help me?

 

[andrewkirk]

Hi, in this link https://math.stackexchange.com/questions/2605752/proof-log-convex-implies-convexity , there is a theorem that labelled with yellow. I do not know the name of theorem and would like to know it's derivation. Could you please help me?

It is the weighted arithmetic mean - geometric mean inequality, and can be proved using Jensen's Inequality. See here.

 

[Niharika]

Yeah, sure it is a weighted arithmetic mean of the functions involved. If you want its detailed explanation then prefer NCERT books.

 

[Ray Vickson]

Yeah, sure it is a weighted arithmetic mean of the functions involved. If you want its detailed explanation then prefer NCERT books.

What is an NCERT book?