Proof of Log Convexity Theorem & Its Derivation

mertcan · Jan 9, 2019

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 · Jan 9, 2019

mertcan said:

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 · Jan 18, 2019

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

Ray Vickson · Jan 24, 2019

Niharika said:

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?

Proof of Log Convexity Theorem & Its Derivation

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