Sherman's and related inequalities with applications in information theory

In this paper we give extensions of Sherman's inequality considering the class of convex functions of higher order. As particular cases, we get an extended weighted majorization inequality as well as Jensen's inequality which have direct connection to information theory. We use the obtained results to derive new estimates for Shannon's and Renyi's entropy, information energy, and some well-known measures between probability distributions. Using the Zipf-Mandelbrot law, we introduce new functionals to derive some related results.

Авторы
Bradanovic S.I.1 , Latif N.2 , Pecaric D.3 , Pecaric J. 4, 5
Редакторы
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Издательство
Springer International Publishing
Номер выпуска
-
Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
-
Ссылка
-
Номер
98
Том
-
Год
2018
Организации
  • 1 Univ Split, Fac Civil Engn Architecture & Geodesy, Split, Croatia
  • 2 Jubail Ind Coll, Dept Gen Studies, Jubail Ind City, Saudi Arabia
  • 3 Catholic Univ Croatia, Zagreb, Croatia
  • 4 Univ Zagreb, Fac Text Technol Zagreb, Zagreb, Croatia
  • 5 RUDN Univ, Moscow, Russia
Ключевые слова
Sherman theorem; Majorization inequality; Jensen inequality; Green function; Abel-Gontscharoff interpolating polynomial; n-convex function; Entropy; Information theory; phi-divergence; Zipf-Mandelbrot law
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7514/