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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 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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    QUALITATIVE BEHAVIOR OF A RATIONAL DIFFERENCE EQUATION
    (CHARLES BABBAGE RES CTR, 2011) Karatas, Ramazan; Gelisken, Ali
    In this paper we study the global behavior of the nonnegative equilibrium points of the difference equation x(n+1) = ax(n-k)/b + cx(n-k)(r)x(n-(2k+1))(s), n = 0, 1 ... where a, b, c are nonnegative parameters, initial conditions are nonnegative real numbers, k is a nonnegative integer and r, s (>=) 1.