학술논문
Sherman's functional, its properties with applications for $f$-divergence measure.
Document Type
Journal
Author
Ivelić Bradanović, Slavica (CT-SPLCAG) AMS Author Profile; Pečarić, Đilda (CT-UNIN2) AMS Author Profile; Pečarić, Josip (CT-HAZU) AMS Author Profile
Source
Subject
15 Linear and multilinear algebra; matrix theory -- 15B Special matrices
15B51Stochastic matrices
26Real functions -- 26D Inequalities
26D15Inequalities for sums, series and integrals
15B51
26
26D15
Language
English
Abstract
In this paper, the authors define Sherman's functional deduced from Sherman's inequality. They establish lower and upper bounds for Sherman's functional and study its properties. As consequences of the main results, they obtain new bounds for Csiszár $f$-divergence functionals and, as special cases, bounds for Shannon's entropy. As applications, the authors use the Zipf-Mandelbrot law to introduce a new entropy and to derive some related results.