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Study of Log Convex Mappings in Fuzzy Aunnam Calculus via Fuzzy Inclusion Relation over Fuzzy-Number Space

Author

Listed:
  • Tareq Saeed

    (Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Muhammad Bilal Khan

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

  • Savin Treanță

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

  • Hamed H. Alsulami

    (Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Mohammed Sh. Alhodaly

    (Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, with the use of newly defined class up and down log–convex fuzzy-number valued mappings, we offer a few new and original mappings defined by applying some mild restrictions over the definition of up and down log–convex fuzzy-number valued mapping. With the use of these mappings, we are able to develop partners of Fejér-type inequalities for up and down log–convexity, which improve upon certain previously established findings. The discussion also includes these mappings’ characteristics. Moreover, some nontrivial examples are also provided to prove the validation of our main results.

Suggested Citation

  • Tareq Saeed & Muhammad Bilal Khan & Savin Treanță & Hamed H. Alsulami & Mohammed Sh. Alhodaly, 2023. "Study of Log Convex Mappings in Fuzzy Aunnam Calculus via Fuzzy Inclusion Relation over Fuzzy-Number Space," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2043-:d:1132768
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    References listed on IDEAS

    as
    1. Yu-Ming Chu & Miao-Kun Wang, 2012. "Inequalities between Arithmetic-Geometric, Gini, and Toader Means," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, December.
    2. 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.
    3. Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "A Sharp Double Inequality between Harmonic and Identric Means," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-7, October.
    4. 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).
    5. Wei-Ming Gong & Ying-Qing Song & Miao-Kun Wang & Yu-Ming Chu, 2012. "A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, September.
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