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Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates

Author

Listed:
  • Muhammad Bilal Khan

    (Department of Mathematics and Computer Science, Transilvania University of Brasov, 29 Eroilor Boulevard, 500036 Brasov, Romania)

  • Eze R. Nwaeze

    (Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA)

  • Cheng-Chi Lee

    (Department of Library and Information Science, Fu Jen Catholic University, New Taipei City 24205, Taiwan
    Department of Computer Science and Information Engineering, Fintech and Blockchain Research Center, Asia University, Taichung City 41354, Taiwan)

  • Hatim Ghazi Zaini

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

  • Der-Chyuan Lou

    (Department of Computer Science and Information Engineering, Chang Gung University, Stroke Center and Department of Neurology, Chang Gung Memorial Hospital at Linkou, Taoyuan 33302, Taiwan)

  • Khalil Hadi Hakami

    (Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia)

Abstract

Due to its significant influence on numerous areas of mathematics and practical sciences, the theory of integral inequality has attracted a lot of interest. Convexity has undergone several improvements, generalizations, and extensions over time in an effort to produce more accurate variations of known findings. This article’s main goal is to introduce a new class of convexity as well as to prove several Hermite–Hadamard type interval-valued integral inequalities in the fractional domain. First, we put forth the new notion of generalized convexity mappings, which is defined as U D - Ԓ -convexity on coordinates with regard to fuzzy-number-valued mappings and the up and down ( U D ) fuzzy relation. The generic qualities of this class make it novel. By taking into account different values for Ԓ , we produce several known classes of convexity. Additionally, we create some new fractional variations of the Hermite–Hadamard ( H H ) and Pachpatte types of inequalities using the concepts of coordinated U D - Ԓ -convexity and double Riemann–Liouville fractional operators. The results attained here are the most cohesive versions of previous findings. To demonstrate the importance of the key findings, we offer a number of concrete examples.

Suggested Citation

  • Muhammad Bilal Khan & Eze R. Nwaeze & Cheng-Chi Lee & Hatim Ghazi Zaini & Der-Chyuan Lou & Khalil Hadi Hakami, 2023. "Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates," Mathematics, MDPI, vol. 11(24), pages 1-27, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4974-:d:1301459
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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.
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    3. Humaira Kalsoom & Muhammad Aamir Ali & Muhammad Idrees & Praveen Agarwal & Muhammad Arif, 2021. "New Post Quantum Analogues of Hermite–Hadamard Type Inequalities for Interval-Valued Convex Functions," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, June.
    4. Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Ahmet Ocak Akdemir & Saad Ihsan Butt & Muhammad Nadeem & Maria Alessandra Ragusa, 2021. "New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
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    7. 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).
    8. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
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