The discussion revolves around the derivation of a theorem related to log convexity and its implications, specifically focusing on the weighted arithmetic mean - geometric mean inequality and its proof using Jensen's Inequality. Participants seek clarification on the theorem's name and derivation.
Participants generally agree on the identification of the theorem as the weighted arithmetic mean - geometric mean inequality, but the discussion remains unresolved regarding the detailed derivation and the specific content of NCERT books.
There are limitations in the discussion regarding the assumptions underlying the theorem and the specific steps involved in the proof, which remain unresolved.
It is the weighted arithmetic mean - geometric mean inequality, and can be proved using Jensen's Inequality. See here.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?
Niharika said:Yeah, sure it is a weighted arithmetic mean of the functions involved. If you want its detailed explanation then prefer NCERT books.