1. Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates.
- Author
-
Khan, Muhammad Bilal, Nwaeze, Eze R., Lee, Cheng-Chi, Zaini, Hatim Ghazi, Lou, Der-Chyuan, and Hakami, Khalil Hadi
- Subjects
- *
INTEGRAL inequalities , *FRACTIONAL integrals , *CONVEXITY spaces , *FUZZY numbers , *SET-valued maps - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF