Improvements of Slater’s Inequality by Means of 4-Convexity and Its Applications

Xuexiao You, Muhammad Adil Khan, Hidayat Ullah and Tareq Saeed
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Xuexiao You: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
Muhammad Adil Khan: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Hidayat Ullah: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Tareq Saeed: Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 8, 1-19

Abstract: In 2021, Ullah et al., introduced a new approach for the derivation of results for Jensen’s inequality. The purpose of this article, is to use the same technique and to derive improvements of Slater’s inequality. The planned improvements are demonstrated in both discrete as well as in integral versions. The quoted results allow us to provide relationships for the power means. Moreover, with the help of established results, we present some estimates for the Csiszár and Kullback–Leibler divergences, Shannon entropy, and Bhattacharyya coefficient. In addition, we discuss some additional applications of the main results for the Zipf–Mandelbrot entropy.

Keywords: convex function; Slater’s inequality; Jensen’s inequality; power mean; information theory; Zipf–Mandelbrot entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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