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

Ammara Nosheen, Khuram Ali Khan, Mariam Aslam, Atiq ur Rehman and Demco K. Mukongo

Journal of Mathematics, 2026, vol. 2026, 1-14

Abstract: This paper investigates the class of interval-valued s-convex functions in the second sense sIVC2 using Caputo–Fabrizio CF integrals. Some generalizations of the Hermite–Hadamard HH-type, Hermite–Hadamard–Fejér HHF-type, and Hermite–Hadamard–Mercer HHM-type inclusions involving the CF 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 HHM-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 RVC and IVC functions, respectively. These results might open the path for new avenues in modeling, optimization problems, interval differential equations, and fuzzy IV functions that involve both discrete and continuous variables simultaneously.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6574276

DOI: 10.1155/jom/6574276

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