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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 Open Access Harmonic mappings for which co-analytic part is a close-to-convex function of order b(Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 2015-01-16) Kahramaner, Yasemin; Aydoğan, Seher Melike; POLATOĞLU, YAŞAR; 199370; 8366; 35549In 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).Publication 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 Embargo Harmonic mappings related to the convex functions(2014) Yemişci, Halime Arzu; POLATOĞLU, YAŞAR; 112614; 199370The main purpose of this paper is to give the extent idea which was introduced by R. M. Robinson [5]. One of the interesting application of this extent idea is an investigation of the class of harmonic mappings related to the convex functions.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 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 Harmonic mappings related to Janowski starlike functions(Elsevier Science Bv, Po Box 211, 1000 Ae Amsterdam, Netherlands, 2014-11) Kahramaner, Yasemin; Aydoğan, Melike; POLATOĞLU, YAŞAR; 8366; 199370; 35549The 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. (C) 2014 Elsevier B.V. All rights reserved.