Naslov
On Sherman’s inequality with applications in information theory

Autori
Barbir, Ana ; Ivelić Bradanović, Slavica ; Pečarić, Ðilda ; Pečarić, Josip

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Inequalities and Zipf-Mandelbrot law. Selected topics in information theory, Monographs in inequalities 15

Urednik/ci
Pečarić, Ðilda ; Pečarić, Josip

Izdavač
Element

Grad
Zagreb

Godina
2019

Raspon stranica
257-286

ISBN
978-953197-670-1

Ključne riječi
Sherman’s inequality, Shannon’s entropy, Zipf-Mandelbrot law

Sažetak
In this paper we proved a converse to Sherman’s inequality. Using the concept of f -divergence we obtained a converse to the Csisz´ar-K¨orner inequality and some inequalities for the well-known entropies. We also established a new lower and upper bounds for Sherman’s inequality as well as for f -divergence functional using some basic convexity facts. As special cases and corollaries of obtained bounds we establishe lower and upper bounds for Shannon’s entropy and relative entropy also known as the Kullback-Leibler divergence. We also introduced a new entropy by applying the Zipf-Mandelbrot law and derived some related inequalities.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Interdisciplinarne prirodne znanosti, Informacijske i komunikacijske znanosti, Interdisciplinarne društvene znanosti

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