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Hermite–Hadamard and Pachpatte Type Inequalities for Coordinated Preinvex Fuzzy-Interval-Valued Functions Pertaining to a Fuzzy-Interval Double Integral Operator

Author

Listed:
  • Gustavo Santos-García

    (Facultad de Economía y Empresa, Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain)

  • Muhammad Bilal Khan

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

  • Hleil Alrweili

    (Department of Mathematics, Faculty of Art and Science, Northern Border University, Rafha, Saudi Arabia)

  • Ahmad Aziz Alahmadi

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

  • Sherif S. M. Ghoneim

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

Abstract

Many authors have recently examined the relationship between symmetry and generalized convexity. Generalized convexity and symmetry have become a new area of study in the field of inequalities as a result of this close relationship. In this article, we introduce the idea of preinvex fuzzy-interval-valued functions (preinvex F∙I-V∙F) on coordinates in a rectangle drawn on a plane and show that these functions have Hermite–Hadamard-type inclusions. We also develop Hermite–Hadamard-type inclusions for the combination of two coordinated preinvex functions with interval values. The weighted Hermite–Hadamard-type inclusions for products of coordinated convex interval-valued functions discussed in a recent publication by Khan et al. in 2022 served as the inspiration for our conclusions. Our proven results expand and generalize several previous findings made in the body of literature. Additionally, we offer appropriate examples to corroborate our theoretical main findings.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2756-:d:879434
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    References listed on IDEAS

    as
    1. Mihai, Marcela V. & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some integral inequalities for harmonic h-convex functions involving hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 257-262.
    2. 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.
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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. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals," Mathematics, MDPI, vol. 10(18), pages 1-18, September.
    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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