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Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

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  • Yongping Deng
  • Hidayat Ullah
  • Muhammad Adil Khan
  • Sajid Iqbal
  • Shanhe Wu
  • Georgios Psarrakos

Abstract

In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:1951799
    DOI: 10.1155/2021/1951799
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    Cited by:

    1. Muhammad Adil Khan & Asadullah Sohail & Hidayat Ullah & Tareq Saeed, 2023. "Estimations of the Jensen Gap and Their Applications Based on 6-Convexity," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    2. 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.

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