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Some New Versions of Integral Inequalities for Left and Right Preinvex Functions in the Interval-Valued Settings

Author

Listed:
  • Muhammad Bilal Khan

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan)

  • Savin TreanțĒŽ

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Mohamed S. Soliman

    (Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Kamsing Nonlaopon

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Hatim Ghazi Zaini

    (Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

Abstract

The principles of convexity and symmetry are inextricably linked. Because of the considerable association that has emerged between the two in recent years, we may apply what we learn from one to the other. In this paper, our aim is to establish the relation between integral inequalities and interval-valued functions ( IV-Fs ) based upon the pseudo-order relation. Firstly, we discuss the properties of left and right preinvex interval-valued functions (left and right preinvex IV-Fs ). Then, we obtain Hermiteā€“Hadamard (š“—-š“—) and Hermiteā€“Hadamardā€“FejĆ©r (š“—-š“—-FejĆ©r) type inequality and some related integral inequalities with the support of left and right preinvex IV-Fs via pseudo-order relation and interval Riemann integral. Moreover, some exceptional special cases are also discussed. Some useful examples are also given to prove the validity of our main results.

Suggested Citation

  • Muhammad Bilal Khan & Savin TreanțĒŽ & 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:611-:d:751235
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    References listed on IDEAS

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    1. Yanrong An & Guoju Ye & Dafang Zhao & Wei Liu, 2019. "Hermite-Hadamard Type Inequalities for Interval ( h 1 , h 2 )-Convex Functions," Mathematics, MDPI, vol. 7(5), pages 1-9, May.
    2. Wei Wei & H. M. Srivastava & Yunyi Zhang & Lei Wang & Peiyi Shen & Jing Zhang, 2014. "A Local Fractional Integral Inequality on Fractal Space Analogous to Andersonā€™s Inequality," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
    3. Priyanka Roy & Geetanjali Panda, 2019. "Expansion of Generalized Hukuhara Differentiable Interval Valued Function," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 553-570, November.
    4. A. K. Bhurjee & G. Panda, 2016. "Sufficient optimality conditions and duality theory for interval optimization problem," Annals of Operations Research, Springer, vol. 243(1), pages 335-348, August.
    5. A. Bhurjee & G. Panda, 2012. "Efficient solution of interval optimization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft fĆ¼r Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 273-288, December.
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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.
    2. Muhammad Bilal Khan & Ali Althobaiti & Cheng-Chi Lee & Mohamed S. Soliman & Chun-Ta Li, 2023. "Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities," Mathematics, MDPI, vol. 11(13), pages 1-23, June.
    3. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    4. Muhammad Bilal Khan & Gustavo Santos-GarcĆ­a & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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