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 Metadata only Bifurcations of Fibonacci generating functions(PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND, 2007-08) Özer, Mehmet; Cenys, Antanas; Hacıbekiroğlu, Gürsel; Akat, Ercüment; Valaristos, A.; Anagnostopoulos, A. N.; POLATOĞLU, YAŞAR; TR2509; TR199370In this work the dynamic behaviour of the one-dimensional family of maps F-p,F-q(x) = 1/(1 - px - qx(2)) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean. (c) 2006 Elsevier Ltd. All rights reserved.Publication Metadata only On lambda-fractional convex functions(2007) Owa, Shigeyoshi; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 199370; 111202Publication Metadata only The relaxed Newton method derivative: Its dynamics and non-linear properties(PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND, 2008-04-01) Özer, Mehmet; Valaristos, Antonios; Miliou, Amalia N.; Anagnostopoulos, Antonios N.; Cenys, Antanas; Hacibekiroğlu, Gürsel; POLATOĞLU, YAŞAR; TR2509; TR199370; TR116304The dynamic behaviour of the one-dimensional family of maps f(x) = c(2)[(a - 1)x + c(1)](-lambda/(alpha-1)) is examined, for representative values of the control parameters a, c(1), c(2) and lambda. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant a. The maps f(x) are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an x(n) versus lambda plot, an initial exponential decay followed by a bifurcation. The value of lambda at which this bifurcation takes place depends on the values of the parameters a, c(1) and c(2). This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x) undergoing a period doubling. For values of a higher than 1 and at higher values of lambda a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c(1) between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents. (c) 2007 Elsevier Ltd. All rights reserved.Publication Metadata only New distortion theorems for Sakaguchi functions(ELEMENT, R AUSTRIJE 11, 10000 ZAGREB, CROATIA, 2007-10) Çağlar, Mert; POLATOĞLU, YAŞAR; TR199370; TR108339Let A be the class of functions f (z) of the form f (z) = z + Sigma(infinity)(k=2), a(k)z(k) that are analytic in the open unit disk D = {(z) epsilon C | |z| < 1} in 1959, K. Sakaguchi [9] has considered the subclass of A consisting of those f (z) which satisfy Re (zf,(z)/f(z)-f(-z)) > 0, where z E D. We call such a function a "Sakaguchi function", and denote the class of those functions by Ss. Various authors have studied this class ([6, 7, 9, 10]). We obtain new distortion theorems, Koebe domain, k-quasiconformatity, and the radius of convexity for the class S-s.Publication Metadata only Harmonic mappings related to the m-fold starlike functions(Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 Usa, 2015-09-15) Aydoğan, Melike; Kahramaner, Yasemin; POLATOĞLU, YAŞAR; 35549; 199370; 8366In the present paper we will give some properties of the subclass of harmonic mappings which is related to m-fold starlike functions in the open unit disc D = {z parallel to z vertical bar < 1}. Throughout this paper we restrict ourselves to the study of sense-preserving harmonic mappings. We also note that an elegant and complete treatment theory of the harmonic mapping is given in Durens monograph (Duren, 1983). The main aim of us to investigate some properties of the new class of us which represented as in the following form, S*H(m) = {f = h(z) + <(g(z))over bar>vertical bar f is an element of SH(m), g'(z)/h'(z) < b(1)p(z), h(z) is an element of S*(m), p(z) is an element of P-(m)}, where h(z) = z + Sigma(infinity)(n-1) a(mn+1)z(mn+1), g(z) = Sigma(infinity)(n-0) b(mn+1)z(mn+1), vertical bar b(1)vertical bar < 1. Crown Copyright (C) 2014 Published by Elsevier Inc. All rights reserved.Publication Metadata only New class of bounded log-harmonic mappings(2016) Özkan Uçar, Hatice Esra; POLATOĞLU, YAŞAR; 199370Publication Metadata only On quasiconformal harmonic mappings lifting to minimal surfaces(Scientific Technical Research Council Turkey-Tubitak, Ataturk Bulvarı No 221, Kavaklıdere, Tr-06100 Ankara, Turkey, 2013) Taştan, Hakan Mete; POLATOĞLU, YAŞAR; 175835; 199370We prove a growth theorem for a function to belong to the class Sigma(mu; a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L-3. We also obtain some estimates of the Gaussian curvature of. the minimal surfaces in 3-dimensional Euclidean space R-3 and of the spacelike minimal surfaces in L-3.Publication Metadata only Bieberbach-de Branges and Fekete-Szego inequalities for certain families of q-convex and q-close-to-convex functions(2018) Çetinkaya, A.; Ahuja, O.P.; POLATOĞLU, YAŞAR; 199370Publication Metadata only Analyzing the Chaotic Behaviour of the Harmonic Function of Henon-Heiles Potential(Springer-Verlag Berlin, Heidelberger Platz 3, D-14197 Berlin, Germany, 2012-05) Bolcal, Ertuğrul Cem; Karakuş, Cahit; POLATOĞLU, YAŞAR; 111950; 277974; 199370In this work, the chaotic behaviour of Harmonic function of Henon-Heiles Hamiltonian system is computed and analyzed by using multi-dimensional Schwarzian derivative. Moreover, chaotic behaviour of the saddle points in Harmonic function is analyzed by adding a linear potential (bx + ay). The results show that Schwarzian derivative facilitates the computation of the chaotic behaviour of a potential function.Publication Metadata only Some Results on Dynamics of Newton Differential Equation(2005) Özer, Mehmet; Hacibekiroğlu, Gürsel; Valaristos, Antonis; Anagnostopoulos, Antonis N.; POLATOĞLU, YAŞAR; 2509; 199370; 116304In this paper the case where the Newton differential equation defined by the Newton-Raphson iteration method equals a constant (namely 2) is investigated. The dynamics of these functions are examined by showing that the solution function can only be a M�bius transformation in the form of . The result obtained after the iterations carried out for the parameters a = 0.1 and b = 0.01 is the so-called �Fibonacci sequences�.