Improved bounds for the Jensen gap with applications in information theory

Khurshid Ahmad^a, Muhammad Adil Khan^b, Shahid Khan^b, Yu-Ming Chu^c,d,*

ABSTRACT: In this article, we utilize strongly convex functions to improve some upper bounds of Jensen?s gap presented in [IEEE Access 8 (2020):98001?98008, Adv Differ Equ 2020 (2020):333]. This leads us towards the improvement of some existing results around various divergences, the Hermite-Hadamard and H?lder inequalities. We also demonstrate these improvements via numerical experiments. Moreover, some new results are established for the Zipf-Mandelbrot entropy

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^a	Department of Statistics, Islamia College University, Peshawar 25000 Pakistan
^b	Department of Mathematics, University of Peshawar, Peshawar 25000 Pakistan
^c	Department of Mathematics, Huzhou University, Huzhou 313000 China
^d	Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121 China

* Corresponding author, E-mail: chuyuming2005@126.com

Received 4 Nov 2020, Accepted 10 May 2022

Improved bounds for the Jensen gap with applications in information theory

Khurshid Ahmada, Muhammad Adil Khanb, Shahid Khanb, Yu-Ming Chuc,d,*

Khurshid Ahmad^a, Muhammad Adil Khan^b, Shahid Khan^b, Yu-Ming Chu^c,d,*