Open AccessEstimation of f-divergence and Shannon entropy by Bullen type inequalities via Fink’s identity
Author(s) -
Muhammad Adeel,
Khuram Ali Khan,
Đilda Pečarić,
Josip Pečarić
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202527a
Subject(s) - mathematics , divergence (linguistics) , identity (music) , entropy (arrow of time) , pure mathematics , inequality , shannon's source coding theorem , type (biology) , information theory , regular polygon , kullback–leibler divergence , convex function , mathematical analysis , statistics , principle of maximum entropy , binary entropy function , geometry , maximum entropy thermodynamics , linguistics , ecology , philosophy , physics , quantum mechanics , acoustics , biology
By using Fink?s identity some new generalizations of Levinson type inequalities for n-convex functions are obtained. In seek of applications of our results to information theory, new generalizations based on f-divergence estimates are also proven. Moreover, some inequalities for Shannon entropies are deduced as well.