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Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation

Author

Listed:
  • Muhammad Bilal Khan

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Hatim Ghazi Zaini

    (Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • 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)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions ( I - V · Fs ), known as left and right χ -pre-invex interval-valued functions (LR- χ -pre-invex I - V · Fs ). For this class of non-convex I - V · Fs , we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.

Suggested Citation

  • Muhammad Bilal Khan & Hatim Ghazi Zaini & Savin Treanțǎ & Mohamed S. Soliman & Kamsing Nonlaopon, 2022. "Riemann–Liouville Fractional Integral Inequalities for Generalized Pre-Invex Functions of Interval-Valued Settings Based upon Pseudo Order Relation," Mathematics, MDPI, vol. 10(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:204-:d:721226
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    References listed on IDEAS

    as
    1. Feixiang Chen, 2013. "A Note on Hermite-Hadamard Inequalities for Products of Convex Functions," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, December.
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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.
    2. Gustavo Santos-García & Muhammad Bilal Khan & Hleil Alrweili & Ahmad Aziz Alahmadi & Sherif S. M. Ghoneim, 2022. "Hermite–Hadamard and Pachpatte Type Inequalities for Coordinated Preinvex Fuzzy-Interval-Valued Functions Pertaining to a Fuzzy-Interval Double Integral Operator," Mathematics, MDPI, vol. 10(15), pages 1-25, August.
    3. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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