Estimations of the Jensen Gap and Their Applications Based on 6-Convexity-Reference-Cited by-同舟云学术

Estimations of the Jensen Gap and Their Applications Based on 6-Convexity

Published:2023-04-20 Issue:8 Volume:11 Page:1957
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Adil Khan Muhammad¹^ORCID,Sohail Asadullah¹,Ullah Hidayat¹^ORCID,Saeed Tareq²^ORCID

Affiliation:

1. Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

2. Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract

The main purpose of this manuscript is to present some new estimations of the Jensen gap in a discrete sense along with their applications. The proposed estimations for the Jensen gap are provided with the help of the notion of 6-convex functions. Some numerical experiments are performed to determine the significance and correctness of the intended estimates. Several outcomes of the main results are discussed for the Hölder inequality and the power and quasi-arithmetic means. Furthermore, some applications are presented in information theory, which provide some bounds for the divergences, Bhattacharyya coefficient, Shannon entropy, and Zipf–Mandelbrot entropy.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/8/1957/pdf

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