Person: POLATOĞLU, YAŞAR
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Dr. Öğr. Üyesi
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POLATOĞLU
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YAŞAR
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Publication Embargo On generalized Janowski starlike logharmonic(2011) Mohd, Maisarah Haji; Darus, Maslina; Yavuz Duman, Emel; POLATOĞLU, YAŞAR; 199370; 111202In this paper, we consider univalent logharmonic mappings of the form f(z) = zh(z)g(z) defined on the open unit disc with the normalization condition g(0) = 1 and h(0) 6= 0. We investigate the class of generalized Janowski starlike defined by subordination. Further we obtain the bound for the functional h(z)/g(z) for f in this class.Publication Embargo Growth and distortion theorems for multivalent Janowski close-to-convex harmonic functions with shear construction method(Scientific Technical Research Council Turkey-Tubitak, Ataturk Bulvarı No 221, Kavaklıdere, Tr-06100 Ankara, Turkey, 2013) Yavuz Duman, Emel; Ozkan, Hatice Esra; POLATOĞLU, YAŞAR; 199370; 111202In this paper we introduce the class of m-valent Janowski close to convex harmonic functions. Growth and distortion theorems are obtained for this class. Our study is based on the harmonic shear methods for harmonic functions.Publication Metadata only Coefficient Inequality For Perturbed Harmonic Mappings(Pergamon-Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford Ox5 1Gb, England, 2010-08) Çağlar, Mert; Yavuz Duman, Emel; POLATOĞLU, YAŞAR; TR199370; TR108339; TR111202The aim of this work is to give the coefficient inequality for the perturbed harmonic mappings in the open unit disc D. (c) 2010 Elsevier Ltd. All rights reserved.Publication Metadata only Distortion properties of perturbed m-valent Janowski Starlike log-harmonic functions(International Conference on Theory and Applications of Mathematics and Informatics, ICTAMI, 2009) Özkan, H. Esra; Yavuz Duman, Emel; POLATOĞLU, YAŞAR; 199370; 111202Publication Embargo Harmonic mappings for which second dilatation is Janowski functions(2013) Yavuz Duman, Emel; Kahramaner, Yasemin; Darus, Maslina; POLATOĞLU, YAŞAR; 111202; 199370; 8366In the present paper we extend the fundamental property that if h(z) and g(z) are regular functions in the open unit disc D with the properties h(0) = g(0) = 0, h maps D onto many-sheeted region which is starlike with respect to the origin, and Re g ′ (z) h′(z) > 0, then Re g(z) h(z) > 0, introduced by R.J. Libera [5] to the Janowski functions and give some applications of this to the harmonic functions.Publication Metadata only Two point distortion theorems and Koebe domain under the Montel normalization for the subclass of starlike functions(International Symposium on Geometric Function Theory and Applications, GFTA 2011, Babes-Bolyai University, Cluj-Napoca, Romania, 2011) Yavuz Duman, Emel; Özkan, H. Esra; POLATOĞLU, YAŞAR; 111202; 199370Publication Metadata only New subclasses of certain analytic functions(2010) Owa, Shigeyoshi; Yavuz Duman, Emel; Aydoğan, S. M.; POLATOĞLU, YAŞAR; 199370; 111202For certain analytic functions fiz) in the open unit disk U, two subclasses 7ia,S;g) and Q(a,(5;g) associated with some analytic function g{z). Some interesting sufficient conditions for fiz) to be in ^(Q,^;^ ) and Qia,6;g) and some necessary conditions for f{z) belonging to •?{a,S;g) and Q{a,S;g) are considered.Publication Open Access Application of the subordination principle to the multivalent harmonic mappings with shear construction method(2011-06) Yavuz Duman, Emel; Özkan, H. Esra; POLATOĞLU, YAŞARThe harmonic function in the open unit disc D = (z is an element of C vertical bar z vertical bar < 1} can be written as a sum of an analytic and an anti-analytic function. f = h(z) + g(z), where h(z) and g(z) are analytic functions in D, and are called the analytic part and co-analytic part of f, respectively. One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion), because the growth theorem and distortion theorem give the compactness of the classes of these functions. In this paper we consider both of these questions with the shear construction method. (C) 2010 Elsevier Ltd. All rights reserved.Publication Metadata only A Remark on multivalently convex and starlike functions(2007-01) Nunokawa, Mamoru; Owa, Shigeyoshi; Yavuz Duman, Emel; POLATOĞLU, YAŞAR; 199370; 111202Applying the result for certain analytic functions due to M. Nunokawa [Proc. Japan Acad. 68A, 152–153 (1992; Zbl 0773.30020)], some properties for multivalently convex and starlike functions ar discussed.Publication Embargo Growth theorems for perturbated starlike log-harmonic mappings of complex order(2009) Yavuz Duman, Emel; Özkan, H. Esra; POLATOĞLU, YAŞAR; 199370; 111202Let H(D) be the linear space of all analytic functions defined on the open unit disc D = {z ∈ C : |z| < 1}. A sense-preserving logharmonic mapping is the solution of the non-linear elliptic partial differential equation fz¯ = wfz ¡ f /f¢ , where w(z) ∈ H(D) is the second dilatation of f such that |w(z)| < 1 for every z ∈ D. It has been shown that if f is a non-vanishing log-harmonic mapping, then f can be expressed as f = h(z)g(z), where h(z) and g(z) are analytic in D. If f vanishes at z = 0 but it is not identically zero, then f admits the representation f = z|z| 2βh(z)g(z), where Reβ > −1/2, h(z) and g(z) are analytic in D, g(0) = 1, h(0) 6= 0 (see [1], [2], [3]). Let f = zh(z)g(z) be a univalent log-harmonic mapping. We say that f is a starlike log-harmonic mapping of complex order b (b 6= 0, complex) if Re ½ 1 + 1 b µ zfz − zf¯ z¯ f − 1 ¶¾ > 0, z ∈ D. The class of all starlike log-harmonic mappings of complex order b is denoted by S ∗ LH(1 − b). We also note that if zh(z) is a starlike function of complex order b, then the starlike log-harmonic mapping f = zh(z)g(z) will be called a perturbated starlike log-harmonic mapping of complex order b, and the family of such mappings will be denoted by S ∗ LH(p)(1 − b). The aim of this paper is to obtain the growth theorems for the perturbated starlike log-harmonic mappings of complex order.