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Keywords = U·D preinvex fuzzy number-valued mappings

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25 pages, 399 KB  
Article
A New Class of Coordinated Non-Convex Fuzzy-Number-Valued Mappings with Related Inequalities and Their Applications
by Aleksandr Rakhmangulov, A. F. Aljohani, Ali Mubaraki and Saad Althobaiti
Axioms 2024, 13(6), 404; https://doi.org/10.3390/axioms13060404 - 16 Jun 2024
Cited by 2 | Viewed by 1113
Abstract
Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on [...] Read more.
Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann’s integral theory, the Hermite–Hadamard’s type inequalities are introduced for a newly defined class of nonconvex functions, which is known as U·D preinvex fuzzy number-valued mappings (U·D preinvex F·N·V·Ms) on coordinates. Some Pachpatte-type inequalities are also established for the product of two U·D preinvex F·N·V·Ms, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann’s integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
22 pages, 2208 KB  
Article
Up and Down h-Pre-Invex Fuzzy-Number Valued Mappings and Some Certain Fuzzy Integral Inequalities
by Muhammad Bilal Khan, Hatim Ghazi Zaini, Jorge E. Macías-Díaz and Mohamed S. Soliman
Axioms 2023, 12(1), 1; https://doi.org/10.3390/axioms12010001 - 20 Dec 2022
Cited by 9 | Viewed by 1902
Abstract
The objective of the current paper is to incorporate the new class and concepts of convexity and Hermite–Hadamard inequality with the fuzzy Riemann integral operators because almost all classical single-valued and interval-valued convex functions are special cases of fuzzy-number valued convex mappings. Therefore, [...] Read more.
The objective of the current paper is to incorporate the new class and concepts of convexity and Hermite–Hadamard inequality with the fuzzy Riemann integral operators because almost all classical single-valued and interval-valued convex functions are special cases of fuzzy-number valued convex mappings. Therefore, a new class of nonconvex mapping in the fuzzy environment has been defined; up and down h-pre-invex fuzzy-number valued mappings (U.D h-pre-invex F-N∙V∙Ms). With the help of this newly defined class, some new versions of Hermite–Hadamard (HH) type inequalities have been also presented. Moreover, some related inequalities such as HH Fejér- and Pachpatte-type inequalities for U∙D h-pre-invex F-N∙V∙Ms are also introduced. Some exceptional cases have been discussed, which can be seen as applications of the main results. We have provided some nontrivial examples. Finally, we also discuss some future scopes. Full article
(This article belongs to the Special Issue Fractional Calculus - Theory and Applications II)
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