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Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities

Author

Listed:
  • Muhammad Bilal Khan

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

  • Aleksandr Rakhmangulov

    (Department of Logistics and Transportation Systems Management, Nosov Magnitogorsk State Technical University, Magnitogorsk 455000, Russia)

  • Najla Aloraini

    (Department of Mathematics, College of Sciences and Arts Onaizah, Qassim University, P.O. Box 6640, Buraydah 51452, Saudi Arabia)

  • Muhammad Aslam Noor

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

  • Mohamed S. Soliman

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

Abstract

We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued mapping as our main goal in this work. With the help of up and down harmonically fuzzy-number convexity and the fuzzy fractional integral operator, we also show the results for the Hermite–Hadamard ( H – H ) inequality, the Fejér type inequality, and some other related versions of inequalities. Moreover, some examples are also presented to discuss the validity of the main results. The results from the new technique show how the suggested scheme is accurate, adaptable, efficient, and user-friendly.

Suggested Citation

  • Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:656-:d:1049209
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    References listed on IDEAS

    as
    1. Tie-Hong Zhao & Yu-Ming Chu & Hua Wang, 2011. "Logarithmically Complete Monotonicity Properties Relating to the Gamma Function," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, July.
    2. Jin-Fa Cheng & Yu-Ming Chu, 2011. "Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-14, August.
    3. Jin-Fa Cheng & Yu-Ming Chu, 2011. "On the Fractional Difference Equations of Order ( 2 , ð ‘ž )," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, September.
    4. Jin-Fa Cheng & Yu-Ming Chu, 2012. "Fractional Difference Equations with Real Variable," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, December.
    5. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    6. Khan, Muhammad Bilal & Santos-García, Gustavo & Noor, Muhammad Aslam & Soliman, Mohamed S., 2022. "Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Chu, Yu-Ming & Xia, Wei-Feng & Zhang, Xiao-Hui, 2012. "The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 412-421.
    8. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals," Mathematics, MDPI, vol. 10(18), pages 1-18, September.
    9. 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.
    10. Muhammad Bilal Khan & Gustavo Santos-García & 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.
    Full references (including those not matched with items on IDEAS)

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