An Approximation algorithm for the combination of G-variational inequality and fixed point problems

An Approximation algorithm for the combination of G-variational inequality and fixed point problems | 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 An Approximation algorithm for the combination of G-variational inequality and fixed point problems Araya Kheawborisut, Atid Kangtunyakarn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4146914/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 In this paper, we introduce a new problem is called the combination of G-variational inequality problem in a Hilbert space endowed with graphs and an iterative scheme to find a common element of the set of fixed points of a G-nonexpansive mapping and the solution set of the proposed problem. Under suitable assumptions, a strong convergence theorem has been proved in the framework of a Hilbert space endowed with graphs. Applying our main result, we solve the G-minimization problem. We also give examples to support our main results. Mathematics Subject Classification (2010). 47H09, 47H10, 90C99. Keywords. the combination of G-variational inequality problems, fixed point problem, G-inverse strongly monotone mapping. Mathematics Subject Classification (2010). 47H09, 47H10, 90C99. the combination of G-variational inequality problems fixed point problem G-inverse strongly monotone mapping. 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-4146914","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":282883582,"identity":"f5d98bd7-1655-4742-84cf-cf2c962f44d2","order_by":0,"name":"Araya Kheawborisut","email":"","orcid":"","institution":"King Mongkut's Institute of Technology Ladkrabang","correspondingAuthor":false,"prefix":"","firstName":"Araya","middleName":"","lastName":"Kheawborisut","suffix":""},{"id":282883584,"identity":"edae7e2f-8c02-4dea-96f8-88d55156381e","order_by":1,"name":"Atid Kangtunyakarn","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYBACAxjNLwGmJWSI1yI5g4GxAaiFh3gtBjfAWhgIazFnb34mXVFhZ2x8u/n4oxs1FjwM7IePbsCnxbLnmJnkmTPJZmZ3jiU25xwDOownLe0GXofdSDC72dh2wMbsRo5hcw4bUIsEjxl+LfeffwNrMZ4B0vKPGC03eMC2mBlIALXkthGhxbInp/xnw5lkY4kbaYmzc/skeNgI+cWc/fhmw4YKO8P+GckHPud8q5PjZz98DK8WTMBGmvJRMApGwSgYBdgAAPDbR87grUDaAAAAAElFTkSuQmCC","orcid":"","institution":"King Mongkut's Institute of Technology Ladkrabang","correspondingAuthor":true,"prefix":"","firstName":"Atid","middleName":"","lastName":"Kangtunyakarn","suffix":""}],"badges":[],"createdAt":"2024-03-22 04:14:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4146914/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4146914/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":53830397,"identity":"34fc6e3c-588c-4b9a-8f88-53618e70f554","added_by":"auto","created_at":"2024-04-01 04:28:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":313946,"visible":true,"origin":"","legend":"","description":"","filename":"AKGVariational.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4146914/v1_covered_cb0ee88f-5a36-4f55-b8e9-cd0f9cafa7ae.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Approximation algorithm for the combination of G-variational inequality and fixed point problems","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":"the combination of G-variational inequality problems, fixed point problem, G-inverse strongly monotone mapping.","lastPublishedDoi":"10.21203/rs.3.rs-4146914/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4146914/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we introduce a new problem is called the combination of G-variational inequality problem in a Hilbert space endowed with graphs and an iterative scheme to find a common element of the set of fixed points of a G-nonexpansive mapping and the solution set of the proposed problem. Under suitable assumptions, a strong convergence theorem has been proved in the framework of a Hilbert space endowed with graphs. Applying our main result, we solve the G-minimization problem. We also give examples to support our main results. Mathematics Subject Classification (2010). 47H09, 47H10, 90C99. Keywords. the combination of G-variational inequality problems, fixed point problem, G-inverse strongly monotone mapping.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMathematics Subject Classification (2010).\u003c/strong\u003e 47H09, 47H10, 90C99.\u003c/p\u003e","manuscriptTitle":"An Approximation algorithm for the combination of G-variational inequality and fixed point problems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-27 01:12:00","doi":"10.21203/rs.3.rs-4146914/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"69bd21f6-4241-4134-b4ce-572755ca07e0","owner":[],"postedDate":"March 27th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-04-01T04:20:42+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-27 01:12:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4146914","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4146914","identity":"rs-4146914","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}