Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018 pp. 739–753.

Inequalities of the Jensen and Edmundson–Lah–Ribarič Type for Positive Linear Functionals with Applications

Authors: Rozarija Mikić (1), Ðilda Pečarić (2), and Josip Pečarić (3)
Author institution:(1) Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10 000 Zagreb, Croatia
(2) Catholic University of Croatia, Ilica 242, 10 000 Zagreb, Croatia
(3) RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia

Summary:

In this paper we derive some Jensen and Edmundson–Lah–Ribarič type inequalities for positive linear functionals without the assumption about the convexity of the functions that are involved. General results are then applied to generalized f-divergence functional. Examples with Zipf’s law and Zipf–Mandelbrot law are given.

2010 Math. Subj. Class. Primary: 26A16; Secondary: 60E05, 60E15.

Keywords: Jensen inequality, Edmundson–Lah–Ribarič inequality, f-divergence, Kullback–Leibler divergence, Zipf–Mandelbrot law.

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