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Yayın Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions(Elsevier Science Inc, 2018-02-15) Sakar, Fethiye Müge; Aydoğan, Seher MelikeLet's take f(z) = h (z) + <(g(z))over bar> which is an univalent sense-preserving harmonic functions in open unit disc D = {z : vertical bar z vertical bar < 1}. If f (z) fulfills vertical bar w(z)vertical bar = |g'(z)/h'(z)vertical bar < m, where 0 <= m < 1, then f(z) is known m-quasiconformal harmonic function in the unit disc (Kalaj, 2010) [8]. This class is represented by S-H(m).The goal of this study is to introduce certain features of the solution for non- linear partial differential equation <(f)over bar>((z) over bar) = w(z)f(z) when vertical bar w(z)vertical bar < m, w(z) (sic) m(2)(b(1)-z)/m(2)-b(1)z, h(z) is an element of S*(A, B). In such case S*(A, B) is known to be the class for Janowski starlike functions. We will investigate growth theorems, distortion theorems, jacobian bounds and coefficient ineqaulities, convex combination and convolution properties for this subclass.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 Some inequalities which hold for starlike log-harmonic mappings of order alpha(Eudoxus Press, LLC., 2014-04) Özkan Uçar, Hatice Esra; Aydoğan, Seher MelikeLet 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).
