Some inequalities which hold for starlike log-harmonic mappings of order alpha

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dc.authorid0000-0003-3787-5989
dc.authorid0000-0002-4822-9571
dc.contributor.authorÖzkan Uçar, Hatice Esraen_US
dc.contributor.authorAydoğan, Seher Melikeen_US
dc.date.accessioned2015-01-15T23:02:51Z
dc.date.available2015-01-15T23:02:51Z
dc.date.issued2014-04
dc.departmentIşık Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.departmentIşık University, Faculty of Arts and Sciences, Department of Mathematicsen_US
dc.description.abstractLet H(D) be the linear space of all analytic functions defined on the open disc D = {z vertical bar vertical bar z vertical bar < 1}. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation <(f)over bar>((z) over bar) = w (f) over bar /f f(z) where w(z) is an element of H(D) is second dilatation such that vertical bar w(z)vertical bar < 1 for all z is an element of D. It has been shown that if f is a non-vanishing log-harmonic mapping, then f can be expressed as f(z) = h(z)<(g(z))over bar> where h(z) and g(z) are analytic function in D. On the other hand, if f vanishes at z = 0 but it is not identically zero then f admits following representation f(z) = z vertical bar z vertical bar(2 beta) h(z)<(g(z))over bar> where Re beta > -1/2, h and g are analytic in D, g(0) = 1, h(0) not equal 0. Let f = z vertical bar z vertical bar(2 beta) h (g) over bar be a univalent log-harmonic mapping. We say that f is a starlike log-harmonic mapping of order alpha if partial derivative(arg f(re(i theta)))/partial derivative theta = Rezf(z)-(z) over barf((z) over bar)/f > alpha, 0 <= alpha < 1. (for all z is an element of U) and denote by S-lh*(alpha) the set of all starlike log-harmonic mappings of order alpha. The aim of this paper is to define some inequalities of starlike log-harmonic functions of order alpha (0 <= alpha <= 1).en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationÖzkan, H. & Aydoğan, S. M. (2014). Some inequalities which hold for starlike log-harmonic mappings of order alpha. Journal Of Computational Analysis And Applications, 16(3), 478-485.en_US
dc.identifier.endpage485
dc.identifier.issn1521-1398
dc.identifier.issn1572-9206
dc.identifier.issue3
dc.identifier.scopus2-s2.0-84911500976
dc.identifier.scopusqualityQ4
dc.identifier.startpage478
dc.identifier.urihttps://hdl.handle.net/11729/542
dc.identifier.volume16
dc.identifier.wosWOS:000330602500008
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakScience Citation Index Expanded (SCI-EXPANDED)en_US
dc.institutionauthorAydoğan, Seher Melikeen_US
dc.institutionauthorid0000-0002-4822-9571
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherEudoxus Press, LLC.en_US
dc.relation.ispartofJournal of Computational Analysis and Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectDistortion theoremen_US
dc.subjectHarmonicen_US
dc.subjectHarmonic mappingen_US
dc.subjectMapen_US
dc.subjectMarx-Strohhacker inequalityen_US
dc.subjectUnivalent functionsen_US
dc.subjectStarlike log-harmonic functionsen_US
dc.titleSome inequalities which hold for starlike log-harmonic mappings of order alphaen_US
dc.typeArticleen_US
dspace.entity.typePublication

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