Solution of an algebraic linear system of equations using fixed point results in C∗−algebra valued extended Branciari Sb−metric spaces

Solution of an algebraic linear system of equations using fixed point results in C∗−algebra valued extended Branciari Sb−metric spaces | 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 Solution of an algebraic linear system of equations using fixed point results in C ∗ −algebra valued extended Branciari S b −metric spaces Khairul Habib Alam, Yumnam Rohen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2727544/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 Two new types of metric spaces namely C∗−algebra valued Branciari S b −metric space and C∗−algebra valued extended Branciari S b −metric space are introduced in this work, which are a generalization of all known related metric spaces.We explained the generalizations with two examples respectively. There are examples of self-mappings having a unique fixed point, which are concluded using our main theorems. As an application, we used one of our main results to show the existence of a unique solution of an algebraic system of linear equations with a numerical example. Mathematics Subject Classification (2010). Primary 54H25; Secondary 47H10. C∗−algebra C∗−algebra valued Branciari Sb−metric space C∗−algebra valued extended Branciari Sb−metric space 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-2727544","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":186057919,"identity":"ed5750c7-e0e8-4ec6-9cfe-ec5bac7a66c9","order_by":0,"name":"Khairul Habib Alam","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVRIiWNgGAWjYDACdgYGxsYGGzjfgLAWZrCWNNK1HCZBC38z89ONM3ect1s7I4HxwweGw8YEtUgcZjO7ufHM7eRtZw4wS85gOGxG2GGHGcxuPmy7nWx2vIGNmYfhsA1BHfKH2b8BtZxLNjvMQKQWg8M8QIe1HbCD2ULYYYaHecpuzmxLTjA7c7BZcoZBOmHvyx1v33azt83O3uxG8sEPHyqsDRsI6oGCxAYGxgaiIhIO7ElQOwpGwSgYBSMNAACoIz+fGWoDvQAAAABJRU5ErkJggg==","orcid":"","institution":"National Institute of Technology Manipur","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Khairul","middleName":"Habib","lastName":"Alam","suffix":""},{"id":186057920,"identity":"2fc03dba-582f-4ac5-b900-737f2e55a114","order_by":1,"name":"Yumnam Rohen","email":"","orcid":"","institution":"Manipur University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yumnam","middleName":"","lastName":"Rohen","suffix":""}],"badges":[],"createdAt":"2023-03-23 12:29:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2727544/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2727544/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":34833268,"identity":"fa76ee98-9f3a-48ec-82e6-adaa51eb296e","added_by":"auto","created_at":"2023-03-27 03:04:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":233299,"visible":true,"origin":"","legend":"","description":"","filename":"kha.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2727544/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eSolution of an algebraic linear system of equations using fixed point results in C\u003csup\u003e∗\u003c/sup\u003e−algebra valued extended Branciari S\u003csub\u003eb\u003c/sub\u003e−metric spaces\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":"C∗−algebra, C∗−algebra valued Branciari Sb−metric space, C∗−algebra valued extended Branciari Sb−metric space","lastPublishedDoi":"10.21203/rs.3.rs-2727544/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2727544/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTwo new types of metric spaces namely C∗−algebra valued Branciari S\u003csub\u003eb\u003c/sub\u003e−metric space and C∗−algebra valued extended Branciari S\u003csub\u003eb\u003c/sub\u003e−metric space are introduced in this work, which are a generalization of all known related metric spaces.We explained the generalizations with two examples respectively. There are examples of self-mappings having a unique fixed point, which are concluded using our main theorems. As an application, we used one of our main results to show the existence of a unique solution of an algebraic system of linear equations with a numerical example.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMathematics Subject Classification (2010).\u003c/strong\u003e Primary 54H25; Secondary 47H10.\u003c/p\u003e","manuscriptTitle":"Solution of an algebraic linear system of equations using fixed point results in C∗−algebra valued extended Branciari Sb−metric spaces","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-03-27 03:04:31","doi":"10.21203/rs.3.rs-2727544/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":"45422865-aa5f-4ec1-8557-8983f3888c65","owner":[],"postedDate":"March 27th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-03-29T16:59:31+00:00","versionOfRecord":[],"versionCreatedAt":"2023-03-27 03:04:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2727544","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2727544","identity":"rs-2727544","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}