Reverses of jensen’s integral inequality and applications: a survey of recent results

Abstract

Several new reverses of the celebrated Jensen’s inequality for convex functions and Lebesgue integral on measurable spaces are surveyed. Applications for weighted discrete means, to Hölder inequality, Cauchy-Bunyakovsky-Schwarz inequality and for f-divergence measures in information theory are also given. Finally, applications for functions of selfadjoint operators in Hilbert spaces with some examples of interest are also provided.