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Further reverse results for Jensen's discrete inequality and applications in information theory.

Ivan Budimir, Sever S Dragomir, ‎Josip Pečarić

Abstract

Some new inequalities which counterpart Jensen’s discrete inequality and improve the recent results from S.S. DRAGOMIR, "A converse result for Jensen’s discrete inequality via Grüss’ inequality and applications in information theory" and S.S. DRAGOMIR, "A converse of the Jensen inequality for convex mappings of several variables and applications" are given. A related result for generalized means is established. Applications in Information Theory are also provided.

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Key concepts: Converse, Jensen's inequality, Mathematics, Log sum inequality, Inequality, Kantorovich inequality, Rearrangement inequality, Bernoulli's inequality