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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 Some results on a starlike log-harmonic mapping of order alpha(Elsevier Science BV, 2014-01-15) Aydoğan, Seher MelikeLet H(D) be the linear space of all analytic functions defined on the open unit disc D = z is an element of C : vertical bar z vertical bar < 1. A sense preserving log-harmonic mapping is the solution of the non-linear elliptic partial differential equation f(z) = w(z)f(z)(f(z)/f) where w(z) is an element of H (D) is the second dilatation off such that vertical bar w(z)vertical bar < 1 for all z is an element of D.A sense preserving log-harmonic mapping is a solution of the non-linear elliptic partial differential equation fz f((z) over bar)/(f) over bar = w(z).f(z)/f (0.1) where w(z) the second dilatation off and w(z) is an element of H(D), vertical bar w(z)vertical bar < 1 for every 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> (0.2) where h(z) and g(z) are analytic in D with the normalization h(0) not equal 0, g(0) = 1. On the other hand if f vanishes at z = 0, but it is not identically zero, then f admits the following representation f(z) = z.z(2 beta)h(z)<(g(z))over bar> (0.3) where Re beta > -1/2, h(z) and g(z) are analytic in the open disc D with the normalization h(0) not equal 0, g(0) = 1 (Abdulhadi and Bshouty, 1988) [2], (Abdulhadi and Hengartner, 1996) [3].In the present paper, we will give the extent of the idea, which was introduced by Abdulhadi and Bshouty (1988) [2]. One of the interesting applications of this extent idea is an investigation of the subclass of log-harmonic mappings for starlike log-harmonic mappings of order alpha.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 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 An investigation of the certain class of multivalent harmonic mappings(Eudoxus Press, 2016-03) Özkan Uçar, Hatice Esra; Polatoğlu, Yaşar; Aydoğan, Seher MelikeThe main purpose of the present paper is to investigate some properties of the certain class of sense-preserving p-valent harmonic mappings in the open unit disc D = {z is an element of C parallel to z vertical bar < 1}.Yayın Notes on harmonic functions for which the second dilatation is α - spiral(Eudoxus Press, 2015-06) Aydoğan, Seher MelikeIn this study, we consider, f = h + (g) over bar harmonic functions in the unit disc D. By applying S. S. Miller and P. M. Mocanu result, we obtain a new subclass of harmonic functions, such as S-HPST*(alpha, beta) We introduce this new class as defined in the following form, S-HPST*(alpha, beta) = {f = h(z) + <(g(z))over bar>vertical bar f is an element of S-H, h(z) is an element of S* , Re (e(i alpha)g '(z)/h '(z)) > beta,vertical bar alpha vertical bar < pi/2,0 <= beta < (0.1), We also use subordination principle, study on distortion theorems, some numerical examples and coefficient inequalities of this class.Yayın Harmonic mappings for which co-analytic part is a close-to-convex function of order b(Springer International Publishing, 2015-01-16) Polatoğlu, Yaşar; Kahramaner, Yasemin; Aydoğan, Seher MelikeIn the present paper we investigate a class of harmonic mappings for which the second dilatation is a close-to-convex function of complex order b, b is an element of C/{0} (Lashin in Indian J. Pure Appl. Math. 34(7):1101-1108, 2003).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.
