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More Accurate Majorization Inequalities Obtained Via Superquadraticity and Convexity with Application to Entropies

Different terms such as variability, inequality and dispersion, which occur in various engineering problems and scientific fields, in mathematics are most simply described by the concept of majorization, a powerful mathematical tool which allows one to see the existing connections between vectors that can be used. In majorization theory, majorization inequalities play an important role. In this paper, using known properties of superquadratic functions, extensions and improvements of majorization inequalities are obtained. Also their converse inequalities are presented. For superquadratic functions, which are not convex, results analog ones for convex functions are presented. For superquadratic functions which are convex, improvements are given. At the end, applications to φ -divergences are discussed. New estimates for the Rényi entropy are derivated.

Sherman inequality ; majorization inequality ; f-divergences ; entropy ; convex function ; superquadratic function

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