Some Coefficient of Inequility for Subclass Of holomorphic Functions

Some Coefficient of Inequility for Subclass Of holomorphic Functions | 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 Some Coefficient of Inequility for Subclass Of holomorphic Functions Isra Al-shbeil, BISWAJIT RATH, REEM K. ALHEFTHI, D. VAMSHEE KRISHNA, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3954649/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 Since the early twentieth century, the investigation of bound fordeterminant of Hankel matrices in analytic univalent functions has been a focalpoint for mathematical research, providing a rich avenue for the exploration ofgeometric properties. Over the years, numerous researchers have striven to establishupper bounds for determinant of the third order Hankel matrix withinvarious subclasses of analytic univalent functions. While these efforts haveyielded valuable insights, the attainment of sharp bounds remained a challengeuntil Know et al. (2018) achieved an exact estimation of the fourth coefficientin the Carath´eodory class. In more recent developments, investigators haveleveraged this precise estimation of the fourth coefficient, alongside the welldefinedvalues of the second and third coefficients within the Carath´eodoryclass. This breakthrough has empowered them to delineate sharp bounds forthe third Hankel determinant in diverse subclasses of analytic univalent functions.This present study embarks on an exploration of upper bounds for thesecond-order Hankel determinant within the realm of analytic functions, subjectto the normalized conditions of f(0) = 0 and f′(0) = 1. We further extendour investigation to specific sub-classes of holomorphic functions, culminatingin the derivation of sharp bounds for a parameter of particular interest. 2020 Mathematics Subject Classification. 30C45, 30C50. Hankel determinant Upper bound Carathéodory function Holomorphic function. 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-3954649","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":274013395,"identity":"fadb0a2c-5b3c-4da6-a951-017d84184604","order_by":0,"name":"Isra Al-shbeil","email":"","orcid":"","institution":"University of Jordan","correspondingAuthor":false,"prefix":"","firstName":"Isra","middleName":"","lastName":"Al-shbeil","suffix":""},{"id":274013396,"identity":"ef12459a-c801-4a01-91bc-293489d61f14","order_by":1,"name":"BISWAJIT RATH","email":"","orcid":"","institution":"GITAM University","correspondingAuthor":false,"prefix":"","firstName":"BISWAJIT","middleName":"","lastName":"RATH","suffix":""},{"id":274013397,"identity":"9286b0ed-2791-42ac-8da3-eb7104b8005d","order_by":2,"name":"REEM K. 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Over the years, numerous researchers have striven to establishupper bounds for determinant of the third order Hankel matrix withinvarious subclasses of analytic univalent functions. While these efforts haveyielded valuable insights, the attainment of sharp bounds remained a challengeuntil Know et al. (2018) achieved an exact estimation of the fourth coefficientin the Carath´eodory class. In more recent developments, investigators haveleveraged this precise estimation of the fourth coefficient, alongside the welldefinedvalues of the second and third coefficients within the Carath´eodoryclass. This breakthrough has empowered them to delineate sharp bounds forthe third Hankel determinant in diverse subclasses of analytic univalent functions.This present study embarks on an exploration of upper bounds for thesecond-order Hankel determinant within the realm of analytic functions, subjectto the normalized conditions of f(0) = 0 and f′(0) = 1. We further extendour investigation to specific sub-classes of holomorphic functions, culminatingin the derivation of sharp bounds for a parameter of particular interest.\u003c/p\u003e\n\u003cp\u003e2020 Mathematics Subject Classification. 30C45, 30C50.\u003c/p\u003e","manuscriptTitle":"Some Coefficient of Inequility for Subclass Of holomorphic Functions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-22 06:26:00","doi":"10.21203/rs.3.rs-3954649/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":"d259dc1b-a6a4-4ebf-9c17-cdc1be97deda","owner":[],"postedDate":"February 22nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-02-23T09:23:17+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-22 06:26:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3954649","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3954649","identity":"rs-3954649","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}