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Hermite-Hadamard-Type Fractional Inclusions for Interval-Valued Preinvex Functions

Author

Listed:
  • Kin Keung Lai

    (International Business School, Shaanxi Normal University, Xi’an 710119, China)

  • Jaya Bisht

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Nidhi Sharma

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

  • Shashi Kant Mishra

    (Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India)

Abstract

We introduce a new class of interval-valued preinvex functions termed as harmonically h -preinvex interval-valued functions. We establish new inclusion of Hermite–Hadamard for harmonically h -preinvex interval-valued function via interval-valued Riemann–Liouville fractional integrals. Further, we prove fractional Hermite–Hadamard-type inclusions for the product of two harmonically h -preinvex interval-valued functions. In this way, these findings include several well-known results and newly obtained results of the existing literature as special cases. Moreover, applications of the main results are demonstrated by presenting some examples.

Suggested Citation

  • Kin Keung Lai & Jaya Bisht & Nidhi Sharma & Shashi Kant Mishra, 2022. "Hermite-Hadamard-Type Fractional Inclusions for Interval-Valued Preinvex Functions," Mathematics, MDPI, vol. 10(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:264-:d:725860
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    Citations

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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.
    2. Muhammad Bilal Khan & Ali Althobaiti & Cheng-Chi Lee & Mohamed S. Soliman & Chun-Ta Li, 2023. "Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities," Mathematics, MDPI, vol. 11(13), pages 1-23, June.
    3. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    4. Muhammad Bilal Khan & Hakeem A. Othman & Aleksandr Rakhmangulov & Mohamed S. Soliman & Alia M. Alzubaidi, 2023. "Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    5. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.

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