Some New Fractional Inequalities for Coordinated Convexity over Convex Set Pertaining to Fuzzy-Number-Valued Settings Governed by Fractional Integrals - Tareq Saeed; Adriana Cătaș; Muhammad Bilal Khan; Ahmed Mohammed Alshehri (Fractal and Fractional, 2023)
In this study, we first propose some new concepts of coordinated up and down convex mappings with fuzzy-number values. Then, Hermite–Hadamard-type inequalities via coordinated up and down convex fuzzy-number-valued mapping (coordinated <semantics>UD</semantics>-convex <semantics>FNVMs</semantics>) are introduced. By taking the products of two coordinated <semantics>UD</semantics>-convex <semantics>FNVMs</semantics>, Pachpatte-type inequalities are also obtained. Some new conclusions are also derived by making particular decisions with the newly defined inequalities, and it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated using nontrivial examples.