Harmonically M-convex Set-valued Function

Harmonically M-convex Set-valued Function | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Harmonically M-convex Set-valued Function Gabriel Alberto Santana, Maira Valera-López This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4224420/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This research aimed to introduce the concept of harmonically m-convex set-valued functions, which is obtained from the combination of two definitions: harmonically m-convex functions and setvalued functions. In this work some properties and characteristics are developed, as well as a inequality of the Hermite-Hadamard type for such functions. set-valued convex functions Harmonically convex functions Harmonically m-convex functions Hermite-Hadamard type inequality convex analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4224420","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":289467424,"identity":"bd572d85-2bf9-4ca1-8410-33a682011f4d","order_by":0,"name":"Gabriel Alberto Santana","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYJADxgdAgoePWOUSQMxsANLCRooWNhDBQFCLvPvxxx9/1Nyp45/d/Kzya46dDBsD88NHN/BoMTyTY2DMc+yZhMSdY2a3ZbclAx3GZmycg09LQw5DMgPbYQmGGwlmtyW3MQO18LBJ49XS//zBwR//DkvI30j/Viy5rZ6wFnmJBMMG3rbDEgY3cswYP247TFiLgcQbY2bevsOSG2/kFEszbjvOw8ZMwC/y/enAEPt2mF/uRvrGjz+3Vdvzszc/fIzXlgNIHGYeMIlHOdiWBiQO4w8CqkfBKBgFo2BkAgBRpkePmJOrtwAAAABJRU5ErkJggg==","orcid":"","institution":"Central University of Venezuela","correspondingAuthor":true,"prefix":"","firstName":"Gabriel","middleName":"Alberto","lastName":"Santana","suffix":""},{"id":289467425,"identity":"01018a97-7b56-40fe-9f73-c320eb295825","order_by":1,"name":"Maira Valera-López","email":"","orcid":"","institution":"Central University of Venezuela","correspondingAuthor":false,"prefix":"","firstName":"Maira","middleName":"","lastName":"Valera-López","suffix":""}],"badges":[],"createdAt":"2024-04-05 18:15:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4224420/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4224420/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59819657,"identity":"5b1187b3-ce0c-4a43-bc94-6a29e0b36657","added_by":"auto","created_at":"2024-07-08 03:14:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":232125,"visible":true,"origin":"","legend":"","description":"","filename":"Harmonicallymconvexsetvaluedfunctionsvs2.tex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4224420/v1_covered_ee0937d6-e06c-493b-af7b-2a47b1a28b9e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eHarmonically M-convex Set-valued Function\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"set-valued convex functions, Harmonically convex functions, Harmonically m-convex functions, Hermite-Hadamard type inequality, convex analysis","lastPublishedDoi":"10.21203/rs.3.rs-4224420/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4224420/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research aimed to introduce the concept of harmonically m-convex set-valued functions, which is obtained from the combination of two definitions: harmonically m-convex functions and setvalued functions. 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