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

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1957-:d:1128823
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    References listed on IDEAS

    as
    1. Mihai, Marcela V. & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some integral inequalities for harmonic h-convex functions involving hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 257-262.
    2. 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.
    3. repec:kap:iaecre:v:14:y:2008:i:4:p:433-440 is not listed on IDEAS
    4. Samih Azar, 2008. "Jensen’s Inequality in Finance," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 14(4), pages 433-440, November.
    5. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
    6. Muhammad Adil Khan & Hidayat Ullah & Tareq Saeed & Hamed H. Alsulami & Z. M. M. M. Sayed & Ahmed Mohammed Alshehri & Fahd Jarad, 2022. "Estimations of the Slater Gap via Convexity and Its Applications in Information Theory," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-21, July.
    7. 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.
    8. 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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