{"title":"Certain properties of Bazilevi\\(\\breve{c}\\) type univalent class defined through subordination","authors":"T. Panigrahi, S. Jena, R. M. El-Ashwah","doi":"10.1007/s13370-024-01216-2","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper with the aid of subordination, the authors introduce two subclasses of analytic functions denoted by <span>\\({\\mathcal {S}}_{\\alpha , \\beta }(\\lambda )~~(\\alpha ,~\\beta ,~ \\lambda \\in {\\mathbb {R}},~\\alpha <1, \\beta >1, \\lambda \\ge 0)\\)</span> and <span>\\({\\mathcal {G}}(\\lambda )\\)</span> defined in the open unit disk <span>\\({\\mathbb {D}}:=\\{z \\in {\\mathbb {C}}:|z|<1\\}\\)</span>. These subclasses are defined through a certain univalent function <span>\\({\\mathcal {S}}_{\\alpha , \\beta }\\)</span> and the generating function of the Gregory coefficients <span>\\({\\mathcal {G}}(\\lambda )\\)</span>. We determine upper bounds of the initial coefficients, Fekete–Szeg<span>\\(\\ddot{o}\\)</span> functional, Hankel determinant of second order, logarithmic coefficients and inverse coefficients of the functions belongs to these subclasses. Some of the corollaries of the main results are also pointed out.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"35 4","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-024-01216-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01216-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In the present paper with the aid of subordination, the authors introduce two subclasses of analytic functions denoted by \({\mathcal {S}}_{\alpha , \beta }(\lambda )~~(\alpha ,~\beta ,~ \lambda \in {\mathbb {R}},~\alpha <1, \beta >1, \lambda \ge 0)\) and \({\mathcal {G}}(\lambda )\) defined in the open unit disk \({\mathbb {D}}:=\{z \in {\mathbb {C}}:|z|<1\}\). These subclasses are defined through a certain univalent function \({\mathcal {S}}_{\alpha , \beta }\) and the generating function of the Gregory coefficients \({\mathcal {G}}(\lambda )\). We determine upper bounds of the initial coefficients, Fekete–Szeg\(\ddot{o}\) functional, Hankel determinant of second order, logarithmic coefficients and inverse coefficients of the functions belongs to these subclasses. Some of the corollaries of the main results are also pointed out.