A Characterization of Convex Functions

2017/09/25 by Leonetti, Paolo
#25B62 #26A51 #52A07 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.08611

Abstract

Let D be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function f: D→ R∪ \+∞\ is convex if and only if for all x,y ∈ D there exists α=α(x,y) ∈ (0,1) such that f(αx+(1-α)y) ≤ αf(x)+(1-α)f(y).

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