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Some New Generalizations of Integral Inequalities for Harmonical cr -( h 1 , h 2 )-Godunova–Levin Functions and Applications

Author

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  • Tareq Saeed

    (Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Waqar Afzal

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
    Department of Mathematics, Government College University Lahore (GCUL), Lahore 54000, Pakistan)

  • Mujahid Abbas

    (Department of Mathematics, Government College University Lahore (GCUL), Lahore 54000, Pakistan
    Department of Medical Research, China Medical University, Taichung 406040, Taiwan
    Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa)

  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    “Fundamental Sciences Applied in Engineering” Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Manuel De la Sen

    (Institute of Research and Development of Processes, Faculty of Science and Technology, Campus of Leioa, University of the Basque Country (UPV/EHU), 48940 Leioa Bizkaia, Spain)

Abstract

The interval analysis is famous for its ability to deal with uncertain data. This method is useful for addressing models with data that contain inaccuracies. Different concepts are used to handle data uncertainty in an interval analysis, including a pseudo-order relation, inclusion relation, and center–radius (cr)-order relation. This study aims to establish a connection between inequalities and a cr-order relation. In this article, we developed the Hermite–Hadamard ( H . H ) and Jensen-type inequalities using the notion of harmonical ( h 1 , h 2 ) -Godunova–Levin (GL) functions via a cr-order relation which is very novel in the literature. These new definitions have allowed us to identify many classical and novel special cases that illustrate our main findings. It is possible to unify a large number of well-known convex functions using the principle of this type of convexity. Furthermore, for the sake of checking the validity of our main findings, some nontrivial examples are given.

Suggested Citation

  • Tareq Saeed & Waqar Afzal & Mujahid Abbas & Savin Treanţă & Manuel De la Sen, 2022. "Some New Generalizations of Integral Inequalities for Harmonical cr -( h 1 , h 2 )-Godunova–Levin Functions and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4540-:d:989978
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    References listed on IDEAS

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    1. Yanrong An & Guoju Ye & Dafang Zhao & Wei Liu, 2019. "Hermite-Hadamard Type Inequalities for Interval ( h 1 , h 2 )-Convex Functions," Mathematics, MDPI, vol. 7(5), pages 1-9, May.
    2. Waqar Afzal & Alina Alb Lupaş & Khurram Shabbir, 2022. "Hermite–Hadamard and Jensen-Type Inequalities for Harmonical ( h 1 , h 2 )-Godunova–Levin Interval-Valued Functions," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    3. Vuk Stojiljković & Rajagopalan Ramaswamy & Ola A. Ashour Abdelnaby & Stojan Radenović, 2022. "Riemann-Liouville Fractional Inclusions for Convex Functions Using Interval Valued Setting," Mathematics, MDPI, vol. 10(19), pages 1-16, September.
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    Cited by:

    1. Tareq Saeed & Waqar Afzal & Khurram Shabbir & Savin Treanţă & Manuel De la Sen, 2022. "Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for ( h 1 , h 2 )-Convex Functions Pertaining to Total Order Relation," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    2. 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.

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