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

Pietro Cerone, Sever S. Dragomir and Eder Kikianty

Applied Mathematics and Computation, 2015, vol. 266, issue C, 304-315

Abstract: 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.

Keywords: Jensen inequality; Ostrowski inequality; Divergence measure (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:304-315

DOI: 10.1016/j.amc.2015.05.071

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