Refinements of the Jensen Inequality and Estimates of the Jensen Gap Based on Interval-Valued Functions

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dc.contributor.authorDemir, Izzettin
dc.date.accessioned2025-10-11T20:48:48Z
dc.date.available2025-10-11T20:48:48Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractThe significance of the Jensen inequality stems from its impactful and compelling outcomes. As a generalization of classical convexity, it plays a key role in deriving other well-known inequalities such as Hermite-Hadamard, H & ouml;lder, Minkowski, arithmetic-geometric, and Young's inequalities. So, this inequality has become an influential concept in a wide range of scientific fields. Besides, interval analysis provides methods for managing uncertainty in data, making it possible to build mathematical and computer models of various deterministic real-world phenomena. In this paper, taking into account all of these, we first present several refinements of the Jensen inequality for the left and right convex interval-valued functions. We also provide examples with corresponding graphs to demonstrate these refinements more clearly. Next, we adopt a novel approach to derive several bounds for the Jensen gap in integral form using the gH-differentiable interval valued functions as well as various related notions. Moreover, we obtain the proposed bounds by utilizing the renowned Ostrowski inequality. The fundamental benefit of the newly discovered inequalities is that they extend to many known inequalities in the literature, as discussed in this work.en_US
dc.identifier.doi10.1002/mma.11046
dc.identifier.endpage12576en_US
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.issue12en_US
dc.identifier.scopus2-s2.0-105004753047en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage12567en_US
dc.identifier.urihttps://doi.org/10.1002/mma.11046
dc.identifier.urihttps://hdl.handle.net/20.500.12684/22116
dc.identifier.volume48en_US
dc.identifier.wosWOS:001485213900001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorDemir, Izzettin
dc.language.isoenen_US
dc.publisherWileyen_US
dc.relation.ispartofMathematical Methods in the Applied Sciencesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectgeneralized Hukuhara differentiabilityen_US
dc.subjectinterval-valued functionsen_US
dc.subjectJensen inequalityen_US
dc.subjectleft and right convex interval-valued functionen_US
dc.subjectOstrowski inequalityen_US
dc.titleRefinements of the Jensen Inequality and Estimates of the Jensen Gap Based on Interval-Valued Functionsen_US
dc.typeArticleen_US

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