Yazar "Tollu, Durhasan Turgut" seçeneğine göre listele

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    A detailed study on a solvable system related to the linear fractional difference equation
    (Amer Inst Mathematical Sciences-Aims, 2021) Tollu, Durhasan Turgut; Yalcinkaya, Ibrahim; Ahmad, Hijaz; Yao, Shao-Wen
    In this paper, we present a detailed study of the following system of difference equations x(n+1) = a/1+y(n)x(n-1), y(n+1) = b/1+x(n)y(n-1), n is an element of N-0, where the parameters a, b, and the initial values x(-1), x(0), y(-1), Y-0 are arbitrary real numbers such that x(n) and y(n) are defined. We mainly show by using a practical method that the general solution of the above system can be represented by characteristic zeros of the associated third-order linear equation. Also, we characterized the well-defined solutions of the system. Finally, we study long-term behavior of the well-defined solutions by using the obtained representation forms.
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    Fine spectra of triangular triple-band matrices on sequence spaces c and lp, (0 < p < 1)
    (Univ Osijek, Dept Mathematics, 2016) Karaisa, Ali; Asar, Yasin; Tollu, Durhasan Turgut
    The purpose of this study is to determine the fine spectra of the operator for which the corresponding upper and lower triangular matrices A(r, s, t) and B(r, s, t) are on the sequence spaces c and l(p), where (0 < p < 1), respectively. Further, we obtain the approximate point spectrum, defect spectrum and compression spectrum on these spaces. Furthermore, we give the graphical representations of the spectrum of the triangular triple band matrix over the sequence spaces c and l(p).
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    GLOBAL BEHAVIOR OF A THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS OF ORDER THREE
    (Ankara Univ, Fac Sci, 2019) Tollu, Durhasan Turgut; Yalcinkaya, Ibrahim
    In this paper, we investigate the global behavior of the positive solutions of the system of difference equations u(n+1) = alpha(1)u(n-1)/beta(1)+gamma(1)v(n-2)(p) , v(n+1) = alpha(2)v(n-1)/beta(2)+gamma(2)w(n-2)(q) , w(n+1) = alpha(3)w(n-1)/beta(3)+gamma(3)u(n-2)(r) for n is an element of N-0 where the initial conditions u-i, v-i, w-i (i = 0, 1, 2) are non-negative real numbers and the parameters alpha(j), beta(j), gamma(j) (j = 1, 2, 3) and p, q, r are positive real numbers, by extending some results in the literature.
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    Global behavior of two-dimensional difference equations system with two period coefficients
    (Tbilisi Centre Math Sci, 2020) Kara, Merve; Tollu, Durhasan Turgut; Yazlik, Yasin
    In this paper, we investigate the following system of difference equations x(n+1) = alpha(n)/1 + y(n)x(n-1), y(n+1) = beta(n)/1 + x(n)y(n-1), n is an element of N-0, where the sequences (alpha(n))(n is an element of N0), (beta(n))(n is an element of N0) are positive, real and periodic with period two and the initial values x(-1), x(0), y(-1), y(0) are non-negative real numbers. We show that every positive solution of the system is bounded and examine their global behaviors. In addition, we give closed forms of the general solutions of the system by using the change of variables. Finally, we present a numerical example to support our results.
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    ON A GENERAL HOMOGENEOUS THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS
    (Amer Inst Mathematical Sciences-Aims, 2021) Touafek, Nouressadat; Tollu, Durhasan Turgut; Akrour, Youssouf
    In this work, we study the behavior of the solutions of following three-dimensional system of difference equations x(n+1) = f(y(n), y(n-1)), y(n+1) = g (z(n), z(n-1)), z(n+1) = h(x(n), x(n-1)) where n is an element of N-0, the initial values x(-1), x(0), y(-1), y(0) z(-1), z(0) are positive real numbers, the functions f, g, h : (0, +infinity)(2) -> (0, +infinity) are continuous and homogeneous of degree zero. By proving some general convergence theorems, we have established conditions for the global stability of the corresponding unique equilibrium point. We give necessary and sufficient conditions on existence of prime period two solutions of the above mentioned system. Also, we prove a result on oscillatory solutions. As applications of the obtained results, some particular systems of difference equations defined by homogeneous functions of degree zero are investigated. Our results generalize some existing ones in the literature.
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    ON A NONLINEAR FUZZY DIFFERENCE EQUATION
    (Ankara Univ, Fac Sci, 2022) Yalcinkaya, Ibrahim; Caliskan, Vildan; Tollu, Durhasan Turgut
    In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation z(n+1) = Az(n-1)/1 + Z(n-2)(p),n is an element of N-0 where (z(n)) is a sequence of positive fuzzy numbers, A and the initial conditions z(-j) (j = 0, 1,2) are positive fuzzy numbers and p is a positive integer.
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    On a solvable nonlinear difference equation of higher order
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Tollu, Durhasan Turgut; Yazlik, Yasin; Taskara, Necati
    In this paper we consider the following higher-order nonlinear difference equation x(n) = alpha x(n-k) + delta x(n-k)x(n-(k+l))/beta x(n-(k+l)) + gamma x(n-1), n is an element of N-0, where k and l are fixed natural numbers, and the parameters alpha, beta, gamma, delta and the initial values x(-i), i = (1, k +l) over bar, are real numbers such that beta(2) + gamma(2) not equal 0. We solve the above-mentioned equation in closed form and considerably extend some results in the literature. We also determine the asymptotic behavior of solutions and the forbidden set of the initial values using the obtained formulae for the case l = 1.
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    On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
    (Walter De Gruyter Gmbh, 2023) Boulouh, Mounira; Touafek, Nouressadat; Tollu, Durhasan Turgut
    In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.
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    On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
    (Walter De Gruyter Gmbh, 2023) Boulouh, Mounira; Touafek, Nouressadat; Tollu, Durhasan Turgut
    In this work, we present results on the stability, the existence of periodic and oscillatory solutions of a general second order system of difference equations defined by the product of separable homogeneous functions of degree zero. Concrete systems for the obtained results are provided.
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    On a System of k-Difference Equations of Order Three
    (Hindawi Ltd, 2020) Yalcinkaya, Ibrahim; Ahmad, Hijaz; Tollu, Durhasan Turgut; Li, Yong-Min
    In this paper, we deal with the global behavior of the positive solutions of the system of k-difference equations u(n+1)((1)) = (alpha(1)u(n-1)((1))/beta(1) + alpha(1)(u(n-2)((2)))(r1)), u(n+1)((2)) = alpha(2)u(n-1)((2))/beta(2) + alpha(2)(u(n-2)((3)))(r2), ... , u(n+1)((k)) = alpha(k)u(n-1)((k))/beta(k) + alpha(k)(u(n-2)((1)))(rk), n is an element of N-0, where the initial conditions u(-l)((i)) (l = 0, 1, 2) are nonnegative real numbers and the parameters alpha(i), beta(i), gamma(i), and r(i) are positive real numbers for i = 1, 2, ... , k, by extending some results in the literature. By the end of the paper, we give three numerical examples to support our theoretical results related to the system with some restrictions on the parameters.
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    On a two-dimensional nonlinear system of difference equations close to the bilinear system
    (Amer Inst Mathematical Sciences-Aims, 2023) Stevic, Stevo; Tollu, Durhasan Turgut
    We consider the two-dimensional nonlinear system of difference equations xn = xn-k ayn-l + byn-(k+l) cyn-l + dyn-(k+l) , yn = yn-k & alpha;xn-l + & beta;xn-(k+l) , & gamma;xn-l + & delta;xn-(k+l) for n E N0, where the delays k and l are two natural numbers, and the initial values x- j, y- j, 1 < j < k+l, and the parameters a, b, c, d, & alpha;, & beta;, & gamma;, & delta; are real numbers. We show that the system of difference equations is solvable by presenting a method for finding its general solution in detail. Bearing in mind that the system of equations is a natural generalization of the corresponding one-dimensional difference equation, whose special cases appear in the literature from time to time, our main result presented here also generalizes many results therein.
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    On the behavior of the solutions of an abstract system of difference equations
    (Springer Heidelberg, 2022) Boulouh, Mounira; Touafek, Nouressadat; Tollu, Durhasan Turgut
    The aim of the present work is to study of the behavior of the solutions of the following abstract system of difference equations defined by x(n+1) = f(1)(x(n), x(n-1)) + f(2)(Y-n, Yn-1), y(n+1) = g(1)(X-n, Xn-1) g(2)(Y-n, Yn-1) where n is an element of No, the initial values x(-1), x(0), y(-1) and y(0) are positive real numbers, and the functions f(1), f(2), g(1), g(2) : (0, + infinity)(2) -> (0, + infinity) are continuous and homogeneous of degree zero.
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    On the dynamics of a higher-order fuzzy difference equation with rational terms
    (Springer, 2023) Yalcinkaya, Ibrahim; El-Metwally, Hamdy; Bayram, Mustafa; Tollu, Durhasan Turgut
    In this paper, we investigate existence, boundedness, asymptotic behavior and the oscillatory behavior of the positive solutions of the fuzzy difference equation z(n+1) = A + B/z(n-m1) + C/z(n-m2), n is an element of N-0, where (z(n)) is a sequence of positive fuzzy numbers, A, B, C and the initial values z(-j), j = 0, 1,..., s, are positive fuzzy numbers and m(1), m(2) are nonnegative integers with s = max {m(1), m(2)}. By studying this equation, we generalize and improve some results from the literature.
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    On the solutions of a system of max-type difference equations
    (Tbilisi Centre Math Sci, 2021) Akrour, Youssouf; Mesmouli, Mouataz Billah; Tollu, Durhasan Turgut; Touafek, Nouressadat
    In this paper, we give explicit formulas of the solutions of the system of max-type difference equations x(n+1) = max {x(n-1),x(n)y(n-1)/y(n-2)}, y(n+1) = max {y(n-1), y(n)x(n-1)/x(n-2)}, where n >= 0 and the initial values are positive real numbers.
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    Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients
    (Hindawi Ltd, 2020) Tollu, Durhasan Turgut
    This paper is dealt with the following system of difference equations x(n+1) = (a(n)/x(n)) + (b(n)/y(n)), y(n+1) = (c(n)/x(n)) + (d(n)/y(n)), where n is an element of N-0 = N boolean OR {0}, the initial values x(0) and y(0) are the positive real numbers, and the sequences (a(n))(n >= 0), (b(n))(n >= 0), (c(n))(n >= 0), and (d(n))(n >= 0) are two-periodic and positive. The system is an extension of a system where every positive solution is two-periodic or converges to a two-periodic solution. Here, the long-term behavior of positive solutions of the system is examined by using a new method to solve the system.
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    Qualitative behavior of a higher-order fuzzy difference equation
    (American Institute of Mathematical Sciences (AIMS), 2023) Yalçınkaya, İbrahim; Tollu, Durhasan Turgut; Khastan, Alireza; Ahmad, Hijaz; Botmart, Thongchai
    In this paper, we investigate the qualitative behavior of the fuzzy difference equation zn +1 = Azn-s/B + C Pi(s)(i=0) z(n-i) where n is an element of N-0 = N boolean OR{0},(z(n)) is a sequence of positive fuzzy numbers, A; B; C and the initial conditions z j; j = 0; 1, ..., s are positive fuzzy numbers and s is a positive integer. Moreover, two examples are given to verify the e ffectiveness of the results obtained.
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    Solvability of a system of higher order nonlinear difference equations
    (Hacettepe Univ, Fac Sci, 2020) Kara, Merve; Yazlik, Yasin; Tollu, Durhasan Turgut
    In this paper we show that the system of difference equations x(n) = ay(n-k) + d(yn)-k(xn)-(k+l)/bx(n)-(k+l) + cy(n-l), y(n) = ax(n)-k + delta x(n)-ky(n)-(k+l)/beta y(n)-(k+l) +gamma x(n-l), where n is an element of N-0, k and l are positive integers, the parameters a, b, c, d, alpha, beta,gamma, delta are real numbers and the initial values x(-j), y(-j), j = (1, k + l$$) over bar, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.
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    Solvability of a system of higher order nonlinear difference equations
    (Hacettepe Univ, Fac Sci, 2020) Kara, Merve; Yazlik, Yasin; Tollu, Durhasan Turgut
    In this paper we show that the system of difference equations x(n) = ay(n-k) + d(yn)-k(xn)-(k+l)/bx(n)-(k+l) + cy(n-l), y(n) = ax(n)-k + delta x(n)-ky(n)-(k+l)/beta y(n)-(k+l) +gamma x(n-l), where n is an element of N-0, k and l are positive integers, the parameters a, b, c, d, alpha, beta,gamma, delta are real numbers and the initial values x(-j), y(-j), j = (1, k + l$$) over bar, are real numbers, can be solved in the closed form. We also determine the asymptotic behavior of solutions for the case l = 1 and describe the forbidden set of the initial values using the obtained formulas. Our obtained results significantly extend and develop some recent results in the literature.