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Yayın Harmonic function for which the second dilatation is ?-spiral(Springer International Publishing AG, 2012) Aydoğan, Seher Melike; Duman, Emel Yavuz; Polatoğlu, Yaşar; Kahramaner, YaseminLet 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-spiral.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 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 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 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 properties of starlike harmonic mappings(Springer International Publishing AG, 2012) Aydoğan, Seher Melike; Yemişçi, Arzu; Polatoğlu, YaşarA fundamental result of this paper shows that the transformation F=az(h(z+a/1+(a) over barz) + /(h(a) + <(g(a))over bar>(z + a) (1 + (a) over barz) defines a function in S0 HS* whenever f = h( z) + g( z) is S0 HS*, andwewill give an application of this fundamental result. MSC: Primary 30C45; Secondary 30C55
