{"title":"UNIVALENT HARMONIC FUNCTIONS GENERATED BY RUSCHEWEYH DERIVATIVES OF ANALYTIC FUNCTIONS","authors":"O. Ahuja, Subzar Beig, V. Ravichandran","doi":"10.17114/j.aua.2019.59.02","DOIUrl":null,"url":null,"abstract":"For λ ≥ 0, p > 0 and a normalized univalent function f defined on the unit disk D, we consider the harmonic function defined by Tλ,p[f ](z) = Dλf(z) + pz(Dλf(z))′ p+ 1 + Dλf(z)− pz(Dλf(z))′ p+ 1 , z ∈ D, where the operator Dλ is the familiar λ-Ruscheweyh derivative operator. We find some necessary and sufficient conditions for the univalence, starlikeness and convexity as well as the growth estimate of the function Tλ,p[f ]. An extension of the above operator is also given. 2010 Mathematics Subject Classification: 30C45.","PeriodicalId":319629,"journal":{"name":"Acta Universitatis Apulensis","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Universitatis Apulensis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17114/j.aua.2019.59.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
For λ ≥ 0, p > 0 and a normalized univalent function f defined on the unit disk D, we consider the harmonic function defined by Tλ,p[f ](z) = Dλf(z) + pz(Dλf(z))′ p+ 1 + Dλf(z)− pz(Dλf(z))′ p+ 1 , z ∈ D, where the operator Dλ is the familiar λ-Ruscheweyh derivative operator. We find some necessary and sufficient conditions for the univalence, starlikeness and convexity as well as the growth estimate of the function Tλ,p[f ]. An extension of the above operator is also given. 2010 Mathematics Subject Classification: 30C45.
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