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

Muhammad Adil Khan (), Asadullah Sohail, Hidayat Ullah and Tareq Saeed
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Muhammad Adil Khan: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Asadullah Sohail: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Hidayat Ullah: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Tareq Saeed: 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

Mathematics, 2023, vol. 11, issue 8, 1-25

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.

Keywords: convex function; 6-convex function; Jensen’s inequality; Hölder inequality; power means; quasi-arithmetic means; information theory; Zipf–Mandelbrot entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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