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In this paper, we give refinements of the integral form of Jensen’s inequality and the Lah–Ribarič inequality. Using these results, we obtain a refinement of the Hölder inequality and a refinement of some inequalities for integral power means and quasiarithmetic means. We also give applications in information theory, namely, we give some interesting estimates for the integral Csiszár divergence and its important particular cases.

Refinements of the integral form of Jensen’s and the Lah–Ribarič inequalities and applications for Csiszár divergence