Yazar "Cinar, Cengiz" seçeneğine göre listele

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    Global asymptotic stability of a system of difference equations
    (TAYLOR & FRANCIS LTD, 2008) Yalcinkaya, Ibrahim; Cinar, Cengiz; Simsek, Dagistan
    In this article, a sufficient condition is obtained for the global asymptotic stability of the following system of difference equations Z(n+1) = Z(n)t(n-1) + a/Z(n) + t(n-1), t(n+1) = t(n)Z(n-1) + a/t(n) + Z(n-1), n=0,1,2,... where the parameter a is an element of (0, infinity) and the initial values (z(k), t(k)) is an element of(0, infinity) (for k = -1, 0).
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    A note on the periodicity of the Lyness max equation
    (PUSHPA PUBLISHING HOUSE, 2008) Gelisken, Ali; Cinar, Cengiz; Karatas, Ramazan
    We investigate the periodic nature of solutions of a "max-type" difference equation sometimes referred to as the "Lyness max" equation. The equation we consider is x(n+1) = max{x(n), A}/x(n-1). where A is a positive real parameter, x - 1 = A(r-1), and x(0) = A(ro) such that r(-1) and r(0) are positive rational numbers. The results in this paper answer the Open Problem of Grove and Ladas (2005). Copyright (c) 2008 Ali Gelisken et al.
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    On the behavior of positive solutions of the system of rational difference equations xn+1 = xn-1/ynxn-1+1, yn+1 = yn-1/xnyn-1+1
    (PERGAMON-ELSEVIER SCIENCE LTD, 2011) Kurbanli, Abdullah Selcuk; Cinar, Cengiz; Yalcinkaya, Ibrahim
    In this paper, we investigate the positive solutions of the system of difference equations x(n+1) = xn-1/YnXn-1+1, Yn+1 = Yn-1/XnYn-1+1 , where y(0), y(-1), x(0), x(-1) is an element of [0,+infinity). (C) 2010 Elsevier Ltd. All rights reserved.
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    On the dynamics of the recursive sequence x(n+1) = alpha xn-1/beta+gamma Sigma k=1t xn-2k Pi k=1t xn-2k
    (PERGAMON-ELSEVIER SCIENCE LTD, 2011) Erdogan, M. Emre; Cinar, Cengiz; Yalcinkaya, Ibrahim
    In this paper, we investigate the global behavior of the difference equation x(n+1) = alpha x(n-1)/beta+gamma Sigma(t)(k=1) x(n-2k) Pi(t)(k=1) x(n-2k) , n = 0, 1, ... where beta is a positive parameter and a,. are non-negative parameters, with non-negative initial conditions. (C) 2011 Elsevier Ltd. All rights reserved.
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    On the dynamics of the recursive sequence xn+1 = xn-1/beta+gamma xn-2(2)xn-4+gamma xn-2xn-4(2)
    (PERGAMON-ELSEVIER SCIENCE LTD, 2011) Erdogan, M. Emre; Cinar, Cengiz; Yalcinkaya, Ibrahim
    In this paper, we investigate the global behavior of the difference equation x(n+1) = x(n-1)/beta+gamma x(n-2)(2)x(n-4)+gamma x(n-2)x(n-4)(2), n = 0, 1, ... with positive parameters and non-negative initial conditions. (C) 2010 Elsevier Ltd. All rights reserved.
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    On the Global Attractivity of a Max-Type Difference Equation
    (HINDAWI PUBLISHING CORPORATION, 2009) Gelisken, Ali; Cinar, Cengiz
    We investigate asymptotic behavior and periodic nature of positive solutions of the difference equation x(n) = max{A/x(n-1), 1/x(n-3)(alpha)}, n = 0, 1, . . . , where A > 0 and 0 < alpha < 1. We prove that every positive solution of this difference equation approaches (x) over bar = 1 or is eventually periodic with period 2. Copyright (C) 2009
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    On the periodicity of a difference equation with maximum
    (HINDAWI LTD, 2008) Gelisken, Ali; Cinar, Cengiz; Yalcinkaya, Ibrahim
    We investigate the periodic nature of solutions of the max difference equation x(n+1) = max{x(n), A}/(x(n)x(n-1)), n = 0, 1,..., where A is a positive real parameter, and the initial conditions x(-1) = A(r-1) and x(0) = A(r0) such that r(-1) and r(0) are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005). Copyright (c) 2008 Ali Gelisken et al.
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    On the recursive sequence x(n+1) = xn-(5k+9)/1+xn-4xn-9 ... xn-(5k+4)
    (MATHEMATICAL SOC REP CHINA, 2008) Simsek, Dagistan; Cinar, Cengiz; Yalcinkaya, Ibrahim
    In this paper a solution of the following difference equation was investigated x(n+1) = x(n-(5k+9))/1+x(n-4)x(n-9) ... x(n-(5k+4)), n =0, 1, 2, ... where x(-(5k+9)), x(-(5k+8)), ..., x(-1), x(0) is an element of (0, infinity).
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    On the solutions of systems of difference equations
    (HINDAWI PUBLISHING CORPORATION, 2008) Yalcinkaya, Ibrahim; Cinar, Cengiz; Atalay, Muhammet
    We show that every solution of the following system of di. erence equations x(n+1)((1)) = x(n)((2))/(x(n)((2))-1), x(n+1)((2)) = x(n)((3))/(x(n)((3))-1), ..., x(n+1)((k)) = x(n)((1))/(x(n)((1)) - 1) as well as of the system x(n+1)((1))= x(n)((k))/(x(n)((k)) -1), x(n+1)((2)) =x(n)((1))/(x(n)((1))-1), ..., x(n+1)((k))/(x(n)((k-1))-1) is periodic with period 2k if k not equal 0 (mod2), and with period k if k=0 (mod) where the initial values are nonzero real numbers for x(0)((1)), x(0)((2)), ..., x(0)((k)) not equal 1. Copyright (c) 2008. Ibrahim Yalcinkaya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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    On the Solutions of the System of Difference Equations xn+1=max{A/xn,yn/xn}, yn+1=max{A/yn,xn/yn}
    (HINDAWI PUBLISHING CORPORATION, 2009) Simsek, Dagistan; Demir, Bilal; Cinar, Cengiz
    We study the behavior of the solutions of the following system of difference equations x(n+1) = max{A/x(n), y(n)/x(n)}, y(n+1) = max{A/y(n), x(n)/y(n)} where the constant A and the initial conditions are positive real numbers. Copyright (C) 2009 Dagistan Simsek et al.