Işık Üniversitesi Kurumsal Akademik Belleği :: DSpace Angular

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Harmonic function for which the second dilatation is ?-spiral
(Springer International Publishing AG, 2012) Aydoğan, Seher Melike; Duman, Emel Yavuz; Polatoğlu, Yaşar; Kahramaner, Yasemin
Let f = h + (g) over bar be a harmonic function in the unit disc . We will give some properties of f under the condition the second dilatation is alpha-spiral.
Harmonic mappings related to the m-fold starlike functions
(Elsevier Science Inc, 2015-09-15) Aydoğan, Seher Melike; Polatoğlu, Yaşar; Kahramaner, Yasemin
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.