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Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation

Author

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  • Zareen A. Khan
  • Waqar Afzal
  • Mujahid Abbas
  • Kwara Nantomah

Abstract

In this note, we introduce the concept of ℏ‐Godunova–Levin interval‐valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér‐type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of other convex classes. To further support our main findings, we formulated several remarks and nontrivial examples.

Suggested Citation

  • Zareen A. Khan & Waqar Afzal & Mujahid Abbas & Kwara Nantomah, 2025. "Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5570638
    DOI: 10.1155/jom/5570638
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    References listed on IDEAS

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    1. Muhammad Bilal Khan & Savin Treanțǎ & Mohamed S. Soliman & Kamsing Nonlaopon & Hatim Ghazi Zaini, 2022. "Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    2. 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.
    3. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţǎ, Savin, 2023. "Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. 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.
    5. 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.
    6. Xiaoju Zhang & Khurram Shabbir & Waqar Afzal & He Xiao & Dong Lin, 2022. "Hermite–Hadamard and Jensen‐Type Inequalities via Riemann Integral Operator for a Generalized Class of Godunova–Levin Functions," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    7. Waqar Afzal & Mujahid Abbas & Omar Mutab Alsalami, 2024. "Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces," Mathematics, MDPI, vol. 12(16), pages 1-33, August.
    8. Savin Treanţă & Priyanka Mishra & Balendu Bhooshan Upadhyay, 2022. "Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds," Mathematics, MDPI, vol. 10(3), pages 1-15, February.
    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. 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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    12. 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.
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