Abstract
The main objective of this study is to introduce new versions of fractional integral inequalities in fuzzy fractional calculus utilizing the introduced preinvexity. Due to the behavior of its definition, the idea of preinvexity plays a significant role in the subject of inequalities. The concepts of preinvexity and symmetry have a tight connection thanks to the significant correlation that has developed between both in recent years. In this study, we attain the Hermite-Hadamard (H·H) and Hermite-Hadamard-Fejér (H·H Fejér) type inequalities for preinvex fuzzy-interval-valued functions (preinvex F·I·V·Fs) via Condition C and fuzzy Riemann–Liouville fractional integrals. Furthermore, we establish some refinements of fuzzy fractional H·H type inequality. There are also some specific examples of the reported results for various preinvex functions deduced. To support the newly introduced ideal, we have provided some nontrivial and logical examples. The results presented in this research are a significant improvement over earlier results. This paper’s awe-inspiring notions and formidable tools may energize and revitalize future research on this worthwhile and fascinating topic.
Highlights
Publisher’s Note: MDPI stays neu-Convex function theory has a wide range of potential applications in a variety of unique and fascinating disciplines of study
Theorem 3.1 reduces to the result for preinvex F⋅I⋅V⋅F given in
Let Ψ: [u, u + φ(ν, u)] → F0 be a preinvex F⋅I⋅V⋅F with u < ν, whose Θ-levels define the family of I⋅V⋅Fs ΨΘ : [u, u + φ(ν, u)] ⊂ R → KC + are given by ΨΘ (ω) =
Summary
Convex function theory has a wide range of potential applications in a variety of unique and fascinating disciplines of study This theory is useful in a variety of fields, including physics, information theory, coding theory, engineering, optimization, and inequality theory. The concept of convex F⋅Ms from Rn to the set of fuzzy numbers was introduced by Nanda and Kar [18], Syau [19], and Furukawa [20]. Noor [27] proposed and investigated the notion of fuzzy preinvex mapping on the invex set He showed how to express the fuzzy optimality conditions of differentiable preinvex fuzzy mappings using variational inequalities. F⋅I⋅V⋅Fs, higher strongly preinvex F⋅I⋅V⋅Fs, generalized strongly preinvex F⋅I⋅V⋅Fs and characterized their optimality conditions by introducing different variational like inequalities They proposed H⋅H inequalities for strongly preinvex F⋅I⋅V⋅Fs by utilizing fuzzy Riemannian. These integrals are used to derive H⋅H type inequalities for preinvex F⋅I⋅V⋅Fs
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