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Journal of Inequalities and Applications

, 2015:328

First Online: 12 October 2015Received: 08 July 2015Accepted: 22 September 2015

Abstract

We provide new inequalities of Jensen-Ostrowski type, by considering bounds for the magnitude of \\int {\Omega} f\circ g \, d\mu-f \zeta - \int {\Omega }g\, d\mu-\zeta f^{\prime} \zeta -\frac {1}{2}\lambda \int {\Omega} g-\zeta ^{2}\, d\mu\, \\zeta\in a,b\, with various assumptions on the absolutely continuous function \f:a,b ightarrow\mathbb{C}\ and a μ-measurable function g, and a complex number λ. Inequalities of Ostrowski and Jensen type are obtained as special cases, by setting \\lambda=0\ and \\zeta =\int {\Omega}g\, d\mu\, respectively. In particular, we obtain some bounds for the discrepancy in Jensen’s integral inequality. Applications of these inequalities for f-divergence measures are also given.

KeywordsJensen inequality Ostrowski inequality divergence measure discrepancy MSC26D10 26D15 94A17  Download fulltext PDF



Autor: Pietro Cerone - Sever S Dragomir - Eder Kikianty

Fuente: https://link.springer.com/







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