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

Muhammad Bilal Khan (), Eze R. Nwaeze, Cheng-Chi Lee (), Hatim Ghazi Zaini, Lou Der-Chyuan () and Khalil Hadi Hakami
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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
Hatim Ghazi Zaini: Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Lou Der-Chyuan: 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

Mathematics, 2023, vol. 11, issue 24, 1-27

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.

Keywords: fuzzy-number valued mappings; fractional integral; coordinated UD -?-convexity; fractional Hermite–Hadamard inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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