13 sonuçlar
Arama Sonuçları
Listeleniyor 1 - 10 / 13
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 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 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 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.Yayın A certain class of starlike log-harmonic mappings(Elsevier Science BV, 2014-11) Aydoğan, Seher Melike; Polatoğlu, YaşarIn 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).Yayın Some inequalities which hold for starlike log-harmonic mappings of order alpha(Eudoxus Press, LLC., 2014-04) Özkan Uçar, Hatice Esra; Aydoğan, Seher MelikeLet 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).
