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Yayın Positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary conditions(Politechnica University of Bucharest, 2017) Aydoğan, Seher Melike; Nazemi, Sayyedeh Zahra; Rezapour, ShahramWe study the existence and uniqueness of positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary condition. Also, we provide an example to illustrate our main result.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 properties concerning close-to-convexity of certain analytic functions(Springer International Publishing AG, 2012) Nunokawa, Mamoru; Aydoğan, Seher Melike; Kuroki, Kazuo; Yıldız, İsmet; Owa, ShigeyoshiLet f(z) be an analytic function in the open unit disk D normalized with f(0) = 0 and f'(0) = 1. With the help of subordinations, for convex functions f(z) in D, the order of close-to-convexity for f(z) is discussed with some example.Yayın Close-to-convex functions defined by fractional operator(2013) Aydoğan, Seher Melike; Kahramaner, Yasemin; Polatoğlu, YaşarLet S denote the class of functions f(z) = z + a2z2+... analytic and univalent in the open unit disc D = {z ∈ C||z|<1}. Consider the subclass and S* of S, which are the classes ofconvex and starlike functions, respectively. In 1952, W. Kaplan introduced a class of analyticfunctions f(z), called close-to-convex functions, for which there existsφ(Z) ∈ C, depending on f(z) with Re( f′(z)/φ′(z) ) > 0 in , and prove that every close-to-convex function is univalent. The normalized class of close-to-convex functions denoted by K. These classesare related by the proper inclusions C ⊂ S* ⊂ K ⊂ S. In this paper, we generalize the close-to-convex functions and denote K(λ) the class of such functions. Various properties of this class of functions is alos studied.Yayın Harmonic mappings related to Janowski convex functions of complex order b(2013) Aydoğan, Seher Melike; Polatoğlu, Yaşar; Kahramaner, YaseminLet SH be the class of all sense-preserving harmonic mappings in the open unit disc D = {z ∈ ℂ||z| < 1}. In the present paper the authors investigate the properties of the class of harmonic mappings which is based on the generalized of R. J. Libera Theorem [7].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 starlike function of complex order ?(Işık University Press, 2014) Aydoğan, Seher MelikeLet SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ?? n=2 anz?, g(z) = ?? n=1 bnz?} The purpose of this talk is to present some results about harmonic mappings which was introduced by R. M. Robinson [8].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 Some results on a subclass of harmonic mappings of order alpha(Işık University Press, 2014) Varol, Dürdane; Aydoğan, Seher Melike; Owa, ShigeyoshiLet S-H be the class of harmonic mappings defined by S-H - {f - h(z) + <(g(z))over bar> vertical bar h(z) - z + Sigma(infinity)(n=2)a(n)z(n) , g(z) - b(1)z + Sigma(infinity)(n=2) b(n)z(n), b(1) < 1} where h(z) and g(z) are analytic. Additionally f(z) is an element of S-H(alpha) double left right arrow vertical bar zh'(z) - <(zg'(z))over bar>/h(z) + <(g(z))over bar> - 1-(b(1)) over bar /1+(b(1)) over bar vertical bar < vertical bar 1 - <(b(1))over bar>/1 + (b(1)) over bar vertical bar - alpha, z is an element of u, 0 <= alpha < 1 - <(b(1))over bar>/1 + (b(1)) over bar In the present work, by considering the analyticity of the functions defined by R. M. Robinson [7], we discuss the applications to the harmonic mappings.Yayın Notes on starlike log-harmonic functions of order α(2013) Aydoğan, Seher Melike; Duman, Emel Yavuz; Owa, ShigeyoshiFor log-harmonic functions f(z) = zh(z)g(z) in the open unit disk U, two subclasses H*LH(α) and G*LH(α) of S*LH(α) consisting of all starlike log-harmonic functions of order α (0 ≤ α < 1) are considered. The object of the present paper is to discuss some coefficient inequalities for h(z) and g(z).Mathematics Subject Classification: Primary 30C55, Secondary 30C45.
