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Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings

Author

Listed:
  • Yahya Almalki

    (Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia)

  • Waqar Afzal

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

Abstract

The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville) and generalize the various previously published results on set-valued mappings via center and radius order relations using harmonical h -convex functions. First, using these notions, we developed the Hermite–Hadamard ( H – H ) inequality, and then constructed some product form of these inequalities for harmonically convex functions. Moreover, to demonstrate the correctness of these results, we constructed some interesting non-trivial examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4041-:d:1246295
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    References listed on IDEAS

    as
    1. İmdat İşcan, 2014. "On Some New Hermite-Hadamard Type Inequalities for s -Geometrically Convex Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, June.
    2. Chen, Feixiang, 2015. "Extensions of the Hermite–Hadamard inequality for harmonically convex functions via fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 121-128.
    3. Fangfang Shi & Guoju Ye & Dafang Zhao & Wei Liu, 2020. "Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    4. Nidhi Sharma & Rohan Mishra & Abdelouahed Hamdi, 2022. "Hermite-Hadamard type integral inequalities for multidimensional general h-harmonic preinvex stochastic processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(19), pages 6719-6740, October.
    5. 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.
    6. 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.
    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.
    8. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    9. Kin Keung Lai & Jaya Bisht & Nidhi Sharma & Shashi Kant Mishra, 2022. "Hermite-Hadamard-Type Fractional Inclusions for Interval-Valued Preinvex Functions," Mathematics, MDPI, vol. 10(2), pages 1-16, January.
    10. Feixiang Chen & Shanhe Wu, 2014. "Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, August.
    11. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
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    Cited by:

    1. 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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