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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 On approximate solutions for two higher-order Caputo-Fabrizio fractional integro-differential equations(Springer International Publishing AG, 2017-08-03) Aydoğan, Seher Melike; Baleanu, Dumitru; Mousalou, Asef; Rezapour, ShahramWe investigate the existence of solutions for two high-order fractional differential equations including the Caputo-Fabrizio derivative. In this way, we introduce some new tools for obtaining solutions for the high-order equations. Also, we discuss two illustrative examples to confirm the reported results. In this way one gets the possibility of utilizing some continuous or discontinuous mappings as coefficients in the fractional differential equations of higher order.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
