Refinement of Discrete Lah–Ribarič Inequality and Applications on Csiszár Divergence

Abstract

In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities for discrete weighted power means and discrete weighted quasi-arithmetic means are obtained. We also give applications in the information theory; namely, we give some interesting estimations for the discrete Csiszár divergence and for its important special cases.

Keywords

• Lah–Ribarič inequality
• Jensen inequality
• Hölder’s inequalit
• power mean
• quasi-arithmetic mean
• Csiszár divergence