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Yayın Harmonic function for which the second dilatation is ?-spiral(Springer International Publishing AG, 2012) Aydoğan, Seher Melike; Duman, Emel Yavuz; Polatoğlu, Yaşar; Kahramaner, YaseminLet 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.Yayın Harmonic mappings related to Janowski convex functions of complex order b(2013) Aydoğan, Seher Melike; Polatoğlu, Yaşar; Kahramaner, YaseminLet SH be the class of all sense-preserving harmonic mappings in the open unit disc D = {z ∈ ℂ||z| < 1}. In the present paper the authors investigate the properties of the class of harmonic mappings which is based on the generalized of R. J. Libera Theorem [7].Yayın Quasiconformal harmonic mappings related to Janowski alpha-spirallike functions(Amer Inst Physics, 2014) Aydoğan, Seher Melike; Polatoğlu, YaşarLet f = h(z) + g(z) be a univalent sense-preserving harmonic mapping of the open unit disc D = {z/vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical bar = vertical bar g'(z)/h'(z)vertical bar < k, 0 < k < 1 the f is called k-quasiconformal harmonic mapping in D. In the present paper we will give some properties of the class of k-quasiconformal mappings related to Janowski alpha-spirallike functions.Yayın Harmonic mappings related to Janowski starlike functions(Elsevier Science BV, 2014-11) Kahramaner, Yasemin; Polatoğlu, Yaşar; Aydoğan, Seher MelikeThe main purpose of the present paper is to give the extent idea which was introduced by Robinson(1947) [6]. One of the interesting application of this extent idea is an investigation of the class of harmonic mappings related to Janowski starlike functions.Yayın Quasiconformal harmonic mappings related to starlike functions(Eudoxus Press, 2014-07) Polatoğlu, Yaşar; Duman, Emel Yavuz; Kahramaner, Yasemin; Aydoğan, Seher MelikeLet f = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the unit disc D = {z is an element of C parallel to z vertical bar < 1}. If f satisfies the condition vertical bar w(z)vertical bar = vertical bar g'(z)/h'(z)vertical bar < k, (0 <= k < 1), then f is called k-quasiconformal harmonic mapping in D.The aim of this paper is to investigate a subclass of k-quasiconformal harmonic mappings.Yayın Bounded harmonic mappings related to starlike functions(Amer Inst Physics, 2014-12-17) Varol, Dürdane; Aydoğan, Seher Melike; Polatoğlu, YaşarLet f = h(z) + <(g(z))over bar> be a sense-preserving harmonic mapping in the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar 1/b(1) g'(z)/h' (z) - M vertical bar < M, M > 1/2, then f is called bounded harmonic mapping. The main purpose of this paper is to give some properties of the class of bounded harmonic mapping.
