On Improved Simpson-Type Inequalities via Convexity and Generalized Fractional Operators

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dc.contributor.authorAlmoneef, Areej A.
dc.contributor.authorHyder, Abd-Allah
dc.contributor.authorHezenci, Fatih
dc.contributor.authorBudak, Huseyin
dc.date.accessioned2025-10-11T20:48:11Z
dc.date.available2025-10-11T20:48:11Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractIn this work, we develop novel Simpson-type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann-Liouville fractional integrals. Using methodologies such as H & ouml;lder's inequality, the power-mean inequality, and convex function properties, we derive precise bounds for these inequalities. The main contributions include the derivation of Simpson-type inequalities under various convexity conditions and their adaptations for specific cases, such as functions with bounded derivatives and Lipschitz continuity. Special cases, where these inequalities reduce to classical results involving standard integrals, are also explored. Explicitly, clear connections to classical integral inequalities are established for differentiable functions whose derivatives satisfy convexity, boundedness, and Lipschitz conditions. Additionally, future research directions are proposed, emphasizing the broad applicability of these results in fractional calculus and convex analysis.en_US
dc.description.sponsorshipKing Khalid University [RGP.2/163/46, PNURSP2025R337]en_US
dc.description.sponsorshipDeanship of Research and Graduate Studies at King Khalid Universityen_US
dc.description.sponsorshipThe authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through the Research Groups Program under grant (RGP.2/163/46). The authors would like to acknowledge the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R337).en_US
dc.identifier.doi10.1155/jom/6972908
dc.identifier.issn2314-4629
dc.identifier.issn2314-4785
dc.identifier.issue1en_US
dc.identifier.urihttps://doi.org/10.1155/jom/6972908
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21786
dc.identifier.volume2025en_US
dc.identifier.wosWOS:001581845100001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherWileyen_US
dc.relation.ispartofJournal of Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectconvex function analysisen_US
dc.subjectintegral inequality applicationsen_US
dc.subjectSimpson-type inequalitiesen_US
dc.subjecttempered fractional calculusen_US
dc.titleOn Improved Simpson-Type Inequalities via Convexity and Generalized Fractional Operatorsen_US
dc.typeArticleen_US

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