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Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation

Author

Listed:
  • Waqar Afzal
  • Khurram Shabbir
  • Mubashar Arshad
  • Joshua Kiddy K. Asamoah
  • Ahmed M. Galal
  • Ching-Feng Wen

Abstract

In interval analysis, integral inequalities are determined based on different types of order relations, including pseudo, fuzzy, inclusion, and various other partial order relations. By developing a link between center-radius (CR) order relations, it seeks to develop a theory of inequalities with novel estimates. A (CR)-order relation relationship differs from traditional interval-order relationships in that it is calculated as follows: q=qc,qr=q¯+q¯/2,q¯−q¯/2. There are several advantages to using this ordered relationship, including the fact that the inequality terms deduced from it yield much more precise results than any other partial-order relation defined in the literature. This study introduces the concept of harmonical h1,h2-convex functions associated with the center-radius order relations, which is very novel in literature. Applied to uncertainty, the center-radius order relation is an effective tool for studying inequalities. Our first step was to establish the Hermite−Hadamard H.H inequality and then to establish Jensen inequality using these notions. We discuss a few exceptional cases that could have practical applications. Moreover, examples are provided to verify the applicability of the theory developed in the present study.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jjmath:8865992
    DOI: 10.1155/2023/8865992
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    Cited by:

    1. 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.
    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.
    3. 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.

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