We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by the improvements of Young's inequality. We also give a generalized Han's inequality. MSC: 26D15; 94A17
In this paper we introduce quasilinear-type divergences defined by the two-parameter generalization of the logarithm. Jeffreys and Jensen-Shannon divergence are also extended to biparametric forms.
Abstract. We establish upper and lower bounds for the normalized Jensen functional in the context of M [ϕ] ,A -convexity. In connection with these results, a refinement of the triangle inequality is proved.Mathematics subject classification (2010): Primary 26B25, Secondary 26E60, 26D15.
Mass transportation problems appear in various areas of mathematics, their
solutions involving cost convex potentials. Fenchel duality also represents an
important concept for a wide variety of optimization problems, both from the
theoretical and the computational viewpoints. We drew a parallel to the
classical theory of convex functions by investigating the cost convexity and
its connections with the usual convexity. We give a generalization of Jensen's
inequality for cost convex functions.Comment: 10 page
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