Jensen–Ostrowski type inequalities and applications for f-divergence measures

摘要

In this paper, we provide inequalities of Jensen–Ostrowski type, by providing bounds for the magnitude of ∫Ω(f∘g)dμ−f(ζ)−∫Ω(g−ζ)f′∘gdμ+12λ∫Ω(g−ζ)2dμ,for various assumptions on the absolutely continuous function f:[a,b]→C, ζ ∈ [a, b], λ∈C, and a μ-measurable function g on Ω. Special cases are considered to provide some inequalities of Jensen type, as well as Ostrowski type, in measure-theoretic (probabilistic) form. Applications for f-divergence measure in information theory are also considered.