{"title":"On certain subclasses of analytic functions associated with the Carlson–Shaffer operator","authors":"J. Patel, A. Sahoo","doi":"10.1515/UMCSMATH-2015-0007","DOIUrl":null,"url":null,"abstract":"The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class \\(R^{\\lambda}(a,c,A,B)\\) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass \\(\\widetilde {R}^{\\lambda}(a,c, A,B)\\) of \\(R^{\\lambda}(a,c,A,B)\\) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Umcs, Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/UMCSMATH-2015-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class \(R^{\lambda}(a,c,A,B)\) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass \(\widetilde {R}^{\lambda}(a,c, A,B)\) of \(R^{\lambda}(a,c,A,B)\) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.