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A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

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  • Moin-ud-Din Junjua

    (School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China)

  • Ather Qayyum

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

  • Arslan Munir

    (Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal 57000, Pakistan)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Türkiye)

  • Muhammad Mohsen Saleem

    (Department of Mathematics, Pakistan International College Jeddah, Jeddah 23342, Saudi Arabia)

  • Siti Suzlin Supadi

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

Abstract

Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo–Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.

Suggested Citation

  • Moin-ud-Din Junjua & Ather Qayyum & Arslan Munir & Hüseyin Budak & Muhammad Mohsen Saleem & Siti Suzlin Supadi, 2024. "A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications," Mathematics, MDPI, vol. 12(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:478-:d:1332241
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    References listed on IDEAS

    as
    1. Xiaobin Wang & Muhammad Shoaib Saleem & Kiran Naseem Aslam & Xingxing Wu & Tong Zhou & Sunil Kumar, 2020. "On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions," Journal of Mathematics, Hindawi, vol. 2020, pages 1-17, December.
    2. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
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