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Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems

Author

Listed:
  • Abdullah Ali H. Ahmadini

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia)

  • Waqar Afzal

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

  • Mujahid Abbas

    (Department of Mathematics, Government College University, Katchery Road, 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)

  • Elkhateeb S. Aly

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia)

Abstract

This note introduces a new class of preinvexity called ( h 1 , h 2 ) -Godunova-Levin preinvex functions that generalize earlier findings. Based on these notions, we developed Hermite-Hadamard, weighted Fejér, and trapezium type inequalities. Furthermore, we constructed some non-trivial examples in order to verify all the developed results. In addition, we discussed some applications related to the trapezoidal formula, probability density functions, special functions and special means. Lastly, we discussed the importance of order relations and left two open problems for future research. As an additional benefit, we believe that the present work can provide a strong catalyst for enhancing similar existing literature.

Suggested Citation

  • Abdullah Ali H. Ahmadini & Waqar Afzal & Mujahid Abbas & Elkhateeb S. Aly, 2024. "Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems," Mathematics, MDPI, vol. 12(3), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:382-:d:1325800
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    References listed on IDEAS

    as
    1. Shilpi Jain & Khaled Mehrez & Dumitru Baleanu & Praveen Agarwal, 2019. "Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications," Mathematics, MDPI, vol. 7(2), pages 1-12, February.
    2. Gavrea, Bogdan, 2015. "A Hermite–Hadamard type inequality with applications to the estimation of moments of continuous random variables," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 92-98.
    3. Peide Liu & Muhammad Bilal Khan & Muhammad Aslam Noor & Khalida Inayat Noor & Kaleem R. Kazmi, 2021. "On Strongly Generalized Preinvex Fuzzy Mappings," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, April.
    4. Waqar Afzal & Khurram Shabbir & Mubashar Arshad & Joshua Kiddy K. Asamoah & Ahmed M. Galal & Ching-Feng Wen, 2023. "Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation," Journal of Mathematics, Hindawi, vol. 2023, pages 1-14, June.
    5. 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.
    6. Yu, Yuping & Liu, Jun & Du, Tingsong, 2022. "Certain error bounds on the parameterized integral inequalities in the sense of fractal sets," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    7. Xiaoju Zhang & Khurram Shabbir & Waqar Afzal & He Xiao & Dong Lin & Xiaolong Qin, 2022. "Hermite–Hadamard and Jensen-Type Inequalities via Riemann Integral Operator for a Generalized Class of Godunova–Levin Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, August.
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