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Hyers–Ulam Stability of 2 D -Convex Mappings and Some Related New Hermite–Hadamard, Pachpatte, and Fejér Type Integral Inequalities Using Novel Fractional Integral Operators via Totally Interval-Order Relations with Open Problem

Author

Listed:
  • Waqar Afzal

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

  • Daniel Breaz

    (Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania)

  • 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)

  • Luminiţa-Ioana Cotîrlă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania)

  • Zareen A. Khan

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Eleonora Rapeanu

    (Department of Mathematics, “Mircea cel Batran” Naval Academy, 900218 Constanta, Romania)

Abstract

The aim of this paper is to introduce a new type of two-dimensional convexity by using total-order relations. In the first part of this paper, we examine the Hyers–Ulam stability of two-dimensional convex mappings by using the sandwich theorem. Our next step involves the development of Hermite–Hadamard inequality, including its weighted and product forms, by using a novel type of fractional operator having non-singular kernels. Moreover, we develop several nontrivial examples and remarks to demonstrate the validity of our main results. Finally, we examine approximate convex mappings and have left an open problem regarding the best optimal constants for two-dimensional approximate convexity.

Suggested Citation

  • Waqar Afzal & Daniel Breaz & Mujahid Abbas & Luminiţa-Ioana Cotîrlă & Zareen A. Khan & Eleonora Rapeanu, 2024. "Hyers–Ulam Stability of 2 D -Convex Mappings and Some Related New Hermite–Hadamard, Pachpatte, and Fejér Type Integral Inequalities Using Novel Fractional Integral Operators via Totally Interval-Order," Mathematics, MDPI, vol. 12(8), pages 1-34, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1238-:d:1379099
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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