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 Embargo The radius of starlikeness of the certain classes of p-valent functions defined by multiplier transformations(Springer International Publishing, 2008-12) Acu, Mugur; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 199370; 111202The aim of this paper is to give the radius of starlikeness of the certain classes of Open image in new window-valent functions defined by multiplier transformations. The results are obtained by using techniques of Robertson (1953,1963) which was used by Bernardi (1970), Libera (1971), Livingstone (1966), and Goel (1972).Publication Embargo Multivalued starlike functions of complex order(2008) Çağlar, Mert; Owa, Shigeyoshi; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 199370; 111202Let S ∗ λ (1−b)(b 6= 0, complex) denote the class of functions f(z) = z+a2z 2+· · · analytic in the open unit disc D = {z ∈ CPublication 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�.Publication Embargo Lambda-fractional properties of generalized Janowski functions in the unit disc(2008) Çağlar, Mert; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 108339; 108339; 111202For analytic function f(z) = z + a2z 2 + · · · in the open unit disc D, a new fractional operator Dλf(z) is defined. Applying this fractional operator Dλf(z) and the principle of subordination, we give new proofs for some classical results concerning the class S ∗ λ (A, B, α) of functions f(z).Publication Embargo Schwarzian Derivative Revisited(İstanbul Kültür Üniversitesi Yayınları, 2006-12) Çağlar, Mert; Demirer, R. Murat; POLATOĞLU, YAŞAR; TR199370The Boolean-algebraic structure of the so-called Schwarzian derivative is investigated. A sufficient condition for a function of several variables to behave chaotically, which concerns its associated Schwarzian derivative, is also given.Publication Embargo Two points-distortion theorems for multivalued starlike functions(2008) Owa, Shigeyoshi; Nakamura, Yayoi; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 199370; 111202Let A be the class of analytic functions f(z) in the open unit disc U with f(0) = 0 and f (0) = 1. Applying the fractional calculus for f(z) ∈ A, the fractional operator Dλf(z) is defined. Further, a new subclass S∗ λ of A is considered using the fractional operator Dλf(z). The object of the present paper is to consider some properties of f(z) in the class S∗ λ.