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On Sherman’s inequality with applications in information theory (CROSBI ID 76431)

Prilog u knjizi | izvorni znanstveni rad | domaća recenzija

Barbir, Ana ; Ivelić Bradanović, Slavica ; Pečarić, Ðilda ; Pečarić, Josip On Sherman’s inequality with applications in information theory // Inequalities and Zipf-Mandelbrot law. Selected topics in information theory, Monographs in inequalities 15 / Pečarić, Ðilda ; Pečarić, Josip (ur.). Zagreb: Element, 2019. str. 257-286

Podaci o odgovornosti

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

engleski

On Sherman’s inequality with applications in information theory

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.

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

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Podaci o prilogu

257-286.

objavljeno

Podaci o knjizi

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

Pečarić, Ðilda ; Pečarić, Josip

Zagreb: Element

2019.

978-953197-670-1

Povezanost rada

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