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

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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)

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.

Suggested Citation

  • Xuexiao You & Muhammad Adil Khan & Hidayat Ullah & Tareq Saeed, 2022. "Improvements of Slater’s Inequality by Means of 4-Convexity and Its Applications," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1274-:d:792072
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    References listed on IDEAS

    as
    1. Yongping Deng & Hidayat Ullah & Muhammad Adil Khan & Sajid Iqbal & Shanhe Wu & Georgios Psarrakos, 2021. "Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, August.
    2. Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "A Sharp Double Inequality between Harmonic and Identric Means," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-7, October.
    3. S. S. Dragomir, 2012. "Some Slater's Type Inequalities for Convex Functions Defined on Linear Spaces and Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, February.
    4. Hidayat Ullah & Muhammad Adil Khan & Tareq Saeed, 2021. "Determination of Bounds for the Jensen Gap and Its Applications," Mathematics, MDPI, vol. 9(23), pages 1-29, December.
    Full references (including those not matched with items on IDEAS)

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