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Yayın Close-to-convex functions defined by fractional operator(2013) Aydoğan, Seher Melike; Kahramaner, Yasemin; Polatoğlu, YaşarLet S denote the class of functions f(z) = z + a2z2+... analytic and univalent in the open unit disc D = {z ∈ C||z|<1}. Consider the subclass and S* of S, which are the classes ofconvex and starlike functions, respectively. In 1952, W. Kaplan introduced a class of analyticfunctions f(z), called close-to-convex functions, for which there existsφ(Z) ∈ C, depending on f(z) with Re( f′(z)/φ′(z) ) > 0 in , and prove that every close-to-convex function is univalent. The normalized class of close-to-convex functions denoted by K. These classesare related by the proper inclusions C ⊂ S* ⊂ K ⊂ S. In this paper, we generalize the close-to-convex functions and denote K(λ) the class of such functions. Various properties of this class of functions is alos studied.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 Notes on starlike log-harmonic functions of order α(2013) Aydoğan, Seher Melike; Duman, Emel Yavuz; Owa, ShigeyoshiFor log-harmonic functions f(z) = zh(z)g(z) in the open unit disk U, two subclasses H*LH(α) and G*LH(α) of S*LH(α) consisting of all starlike log-harmonic functions of order α (0 ≤ α < 1) are considered. The object of the present paper is to discuss some coefficient inequalities for h(z) and g(z).Mathematics Subject Classification: Primary 30C55, Secondary 30C45.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.
