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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 Harmonic mappings related to starlike function of complex order ?(Işık University Press, 2014) Aydoğan, Seher MelikeLet SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ?? n=2 anz?, g(z) = ?? n=1 bnz?} The purpose of this talk is to present some results about harmonic mappings which was introduced by R. M. Robinson [8].Yayın A certain class of harmonic mappings related to functions of bounded boundary rotation(Eudoxus Press, 2014-05) Polatoğlu, Yaşar; Yavuz Duman, Emel; Aydoğan, Seher MelikeLet V(k) be the class of functions with bounded boundary rotation and let S-H be the class of sense-preserving harmonic mappings. In the present paper we investigate a certain class of harmonic mappings related to the function of bounded boundary rotation.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 Some results on a subclass of harmonic mappings of order alpha(Işık University Press, 2014) Varol, Dürdane; Aydoğan, Seher Melike; Owa, ShigeyoshiLet S-H be the class of harmonic mappings defined by S-H - {f - h(z) + <(g(z))over bar> vertical bar h(z) - z + Sigma(infinity)(n=2)a(n)z(n) , g(z) - b(1)z + Sigma(infinity)(n=2) b(n)z(n), b(1) < 1} where h(z) and g(z) are analytic. Additionally f(z) is an element of S-H(alpha) double left right arrow vertical bar zh'(z) - <(zg'(z))over bar>/h(z) + <(g(z))over bar> - 1-(b(1)) over bar /1+(b(1)) over bar vertical bar < vertical bar 1 - <(b(1))over bar>/1 + (b(1)) over bar vertical bar - alpha, z is an element of u, 0 <= alpha < 1 - <(b(1))over bar>/1 + (b(1)) over bar In the present work, by considering the analyticity of the functions defined by R. M. Robinson [7], we discuss the applications to the harmonic mappings.Yayın Harmonic mappings related to the m-fold starlike functions(Elsevier Science Inc, 2015-09-15) Aydoğan, Seher Melike; Polatoğlu, Yaşar; Kahramaner, YaseminIn 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.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.Yayın On the class of harmonic mappings which is related to the class of bounded boundary rotation(Elsevier Science Inc, 2015-09-15) Polatoğlu, Yaşar; Aydoğan, Seher Melike; Kahramaner, YaseminThe class of bounded radius of rotation is generalization of the convex functions. The concept of functions bounded boundary rotation originated from Loewner (1917). But he did not use the present terminology. It was Paatero (1931, 1933) who systematically developed their properties and made an exhaustive study of the class Vk. In the present paper we will investigate the class of harmonic mappings which is related to the class of bounded boundary rotation.
