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Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions

Author

Listed:
  • Muhammad Bilal Khan

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan)

  • Jorge E. Macías-Díaz

    (Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20131, Mexico
    Department of Mathematics, School of Digital Technologies, Tallinn University, Narva Rd. 25, 10120 Tallinn, Estonia)

  • Savin Treanțǎ

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Mohamed S. Soliman

    (Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

Abstract

The goal of this study is to create new variations of the well-known Hermite–Hadamard inequality ( HH -inequality) for preinvex interval-valued functions (preinvex I-V-F s). We develop several additional inequalities for the class of functions whose product is preinvex I-V-F s. The findings described here would be generalizations of those found in previous studies. Finally, we obtain the Hermite–Hadamard–Fejér inequality with the support of preinvex interval-valued functions. Some new and classical special cases are also obtained. Moreover, some nontrivial examples are given to check the validity of our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3851-:d:945196
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    References listed on IDEAS

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    1. Xia Wu & JinRong Wang & Jialu Zhang, 2019. "Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    2. Khan, Muhammad Bilal & Santos-García, Gustavo & Noor, Muhammad Aslam & Soliman, Mohamed S., 2022. "Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. 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.
    4. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. Wenbing Sun, 2021. "Hermite–Hadamard Type Local Fractional Integral Inequalities With Mittag-Leffler Kernel For Generalized Preinvex Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-13, December.
    6. Tie-Hong Zhao & Wei-Mao Qian & Yu-Ming Chu, 2022. "On approximating the arc lemniscate functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 316-329, June.
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    Cited by:

    1. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    2. Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.

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