Inequalities of the Jensen and Edmundson–Lah–Ribarič type for positive linear functionals with applications

Rozarija Mikić^a, Ðilda Pečarić^b, Josip Pečarić<sup>c

a</sup> Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10 000 Zagreb, Croatia
^b Catholic University of Croatia, Ilica 242, 10 000 Zagreb, Croatia
^c RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia

Abstract: 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.

Key words and phrases: Jensen inequality, Edmundson–Lah–Ribarič inequality, $f$-divergence, Kullback–Leibler divergence, Zipf–Mandelbrot law.

MSC: Primary 26A16; Secondary 60E05, 60E15

Language: English

DOI: 10.17323/1609-4514-2018-18-4-739-753

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