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Harmonic mappings related to the m-fold starlike functions

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Tarih
2015-09-15
Yazarlar
Aydoğan, Melike
Polatoğlu, Yaşar
Kahramaner, Yasemin
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Yayımcı
Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 Usa
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Özet
In the present paper we will give some properties of the subclass of harmonic mappings which is related to m-fold starlike functions in the open unit disc D = {z parallel to z vertical bar < 1}. Throughout this paper we restrict ourselves to the study of sense-preserving harmonic mappings. We also note that an elegant and complete treatment theory of the harmonic mapping is given in Durens monograph (Duren, 1983). The main aim of us to investigate some properties of the new class of us which represented as in the following form, S*H(m) = {f = h(z) + <(g(z))over bar>vertical bar f is an element of SH(m), g'(z)/h'(z) < b(1)p(z), h(z) is an element of S*(m), p(z) is an element of P-(m)}, where h(z) = z + Sigma(infinity)(n-1) a(mn+1)z(mn+1), g(z) = Sigma(infinity)(n-0) b(mn+1)z(mn+1), vertical bar b(1)vertical bar < 1. Crown Copyright (C) 2014 Published by Elsevier Inc. All rights reserved.
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Anahtar kelimeler
m-fold starlike functions, Distortion theorem, Growth theorem
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