Some Novel Inclusions for Interval‐Valued s ‐Convex Functions in the Second Sense Involving Caputo–Fabrizio Integrals

This paper investigates the class of interval‐valued s ‐convex functions in the second sense using Caputo–Fabrizio integrals. Some generalizations of the Hermite–Hadamard ‐type, Hermite–Hadamard–Fejér ‐type, and Hermite–Hadamard–Mercer ‐type inclusions involving the integrals are developed. While the Jensen’s inclusion and Jensen–Mercer‐type inclusion are also formulated for the same class of functions to help developing ‐type inclusion. Additionally, some inclusions for the product of these functions involving these operators are also presented. Substitutions are applied to the main results, yielding corresponding inequalities for real‐valued s ‐convex functions in the second sense and inequalities and inclusions for real‐valued convex and functions, respectively. These results might open the path for new avenues in modeling, optimization problems, interval differential equations, and fuzzy functions that involve both discrete and continuous variables simultaneously.