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Publication Metadata only Harmonic mappings related to the m-fold starlike functions(Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 Usa, 2015-09-15) Aydoğan, Melike; Kahramaner, Yasemin; POLATOĞLU, YAŞAR; 35549; 199370; 8366In 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. Crown Copyright (C) 2014 Published by Elsevier Inc. All rights reserved.Publication Metadata only Some Properties Of Analytic Functions Relating To The Miller And Mocanu Result(Pergamon-Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford Ox5 1Gb, England, 2011-03) Yavuz Duman, Emel; Nunokawa, Mamoru; Owa, Shigeyoshi; Aydoğan, Melike; TR111202; TR35549Let P(alpha) be the class of analytic functions p(z) in the open unit disc U with p(0) = 1 and |arg p(z)| < pi/2 alpha (z is an element of U) for some real alpha > 0. The object of the present paper is to discuss some properties of p(z) in the class P(alpha). Furthermore, an example for our results is shown. (C) 2010 Elsevier Ltd. All rights reserved.Publication Embargo Harmonic Function For Which The Second Dilatation is Alpha-Spiral(Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 2012) Duman Yavuz, Emel; Aydoğan, Melike; Kahramaner, Yasemin; POLATOĞLU, YAŞAR; 111202; 35549; 199370; 8366Let 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-spiralPublication Metadata only On the class of harmonic mappings which is related to the class of bounded boundary rotation(Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 Usa, 2015-09-15) Aydoğan, Melike; Kahramaner, Yasemin; POLATOĞLU, YAŞAR; 199370; 35549; 8366The 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 V-k. In the present paper we will investigate the class of harmonic mappings which is related to the class of bounded boundary rotation. Crown Copyright (C) 2014 Published by Elsevier Inc. All rights reserved.Publication Metadata only A certain class of starlike log-harmonic mappings(Elsevier Science Bv, Po Box 211, 1000 Ae Amsterdam, Netherlands, 2014-11) Aydoğan, Melike; POLATOĞLU, YAŞAR; 35549; 199370In this paper we investigate some properties of log-harmonic starlike mappings. For this aim we use the subordination principle or Lindelof Principle (Lewandowski (1961) [71). (C) 2014 Elsevier B.V. All rights reserved.Publication Metadata only Quasiconformal Harmonic Mappings Related To Starlike Functions(Eudoxus Press, Llc, 1424 Beaver Trail Drive, Cordova, Tn 38016 Usa, 2014-07) Yavuz Duman, Emel; Kahramaner, Yasemin; Aydoğan, Melike; POLATOĞLU, YAŞAR; 199370; 111202; 8366; 35549Let 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.Publication Metadata only Quasiconformal Harmonic Mappings Related to Janowski Alpha-Spirallike Functions(Amer Inst Physics, 2 Huntington Quadrangle, Ste 1No1, Melville, Ny 11747-4501 Usa, 2014) Aydoğan, Melike; POLATOĞLU, YAŞAR; 199370; 35549Let 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.Publication Metadata only A Certain Class of Harmonic Mappings Related to Functions of Bounded Boundary Rotation(Eudoxus Press, Llc, 1424 Beaver Trail Drive, Cordova, Tn 38016 Usa, 2014-05) Yavuz Duman, Emel; Aydoğan, Melike; POLATOĞLU, YAŞAR; 199370; 111202; 35549Let 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.Publication Metadata only Some Inequalities Which Hold For Starlike Log-Harmonic Mappings Of Order Alpha(Eudoxus Press, Llc, 1424 Beaver Trail Drive, Cordova, Tn 38016 Usa, 2014-04) Özkan, Hatice Esra; Aydoğan, Melike; 35549Let 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).Publication Open Access Quasi Subordinations for Bi-Univalent Functions With Symmetric Conjugate Points(Yıldız Technical University, 2024) Sakar, Fethiye Müge; Aydoğan, Melike; KARAHÜSEYİN, ZELİHAMany researchers have recently acquainted and researched several interesting subfamilies of bi-univalent function family delta and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar. In this current work, the subfamily F-delta,q(sc) (alpha, Xi) of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients vertical bar a(2)vertical bar, vertical bar a(3)vertical bar and besides related with these coefficients vertical bar a(3) - a(2)(2)vertical bar for functions belonging to this subfamily are derived. Further some corollaries are also presented.