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A Refined Jensen Inequality Connected to an Arbitrary Positive Finite Sequence

Author

Listed:
  • Shanhe Wu

    (Institute of Applied Mathematics, Longyan University, Longyan 364012, China)

  • Muhammad Adil Khan

    (Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan)

  • Tareq Saeed

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Zaid Mohammed Mohammed Mahdi Sayed

    (Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
    Department of Mathematics, University of Sáadah, Sáadah 1872, Yemen)

Abstract

The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s inequality. As results, we obtain refinements of the quasi-arithmetic and power mean inequalities. Finally, several results are obtained in information theory with the help of the main results.

Suggested Citation

  • Shanhe Wu & Muhammad Adil Khan & Tareq Saeed & Zaid Mohammed Mohammed Mahdi Sayed, 2022. "A Refined Jensen Inequality Connected to an Arbitrary Positive Finite Sequence," Mathematics, MDPI, vol. 10(24), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4817-:d:1007398
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    References listed on IDEAS

    as
    1. Lin, Qian, 2019. "Jensen inequality for superlinear expectations," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 79-83.
    2. repec:kap:iaecre:v:14:y:2008:i:4:p:433-440 is not listed on IDEAS
    3. 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.
    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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