{"title":"Harmonic Mappings With Fixed Analytic Part","authors":"Rajbala Choudary, J. K. Prajapat","doi":"10.2139/ssrn.3316668","DOIUrl":null,"url":null,"abstract":"In this article, we consider a class of sense preserving harmonic mappings having analytic part convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Also, we obtain bounds on the pre-Schwarzian derivatives and on the Bloch’s constant. In addition, we investigate the coefficient estimates, growth and distortion results.","PeriodicalId":443021,"journal":{"name":"Engineering Educator: Courses","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Educator: Courses","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3316668","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In this article, we consider a class of sense preserving harmonic mappings having analytic part convex in one direction. We prove that functions in this class are close-to-convex for certain values of parameters. Also, we obtain bounds on the pre-Schwarzian derivatives and on the Bloch’s constant. In addition, we investigate the coefficient estimates, growth and distortion results.