Showing papers by "Stevo Stević published in 2014"
TL;DR: In this article, generalized Fibonacci sequences and the initial value of the bilinear difference equation are represented as well as some applications concerning a two-dimensional system of BLE equations.
Abstract: Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results in the literature. Some applications concerning a two-dimensional system of bilinear difference equations are also given.
83 citations
TL;DR: In this paper, it was shown that the following system of difference equations, where,,, and sequences,, are real, can be solved in closed form in the case when the sequences,, and are constant and, respectively.
Abstract: We show that the following system of difference equationswhere , , , and sequences , , and are real, can be solved in closed form. For the case when the sequences , , and are constant and , we apply obtained formulas in the investigation of the asymptotic behaviour of well-defined solutions of the system. We also find domain of undefinable solutions of the system. Our results considerably extend and improve some recent results in the literature.
56 citations
TL;DR: The boundedness and compactness of weighted composition operators and a class of integral-type operators recently introduced by S. Stevic and weighted Bergman–Orlicz spaces are characterized.
47 citations
TL;DR: The boundedness character of positive solutions of the next max-type system of difference equations was studied in this article, where it was shown that the boundedness of the positive solutions is bounded by
Abstract: The boundedness character of positive solutions of the next max-type system of difference equations
37 citations
TL;DR: It is shown that under some conditions posed on functions fjijfjij all positive solutions of the system are eventually periodic with period Ts , for some T∈NT∈N.
15 citations
TL;DR: The boundedness character of positive solutions of the following cyclic system of difference equations where A, p and q are positive numbers, and where if, for some and, then denotes, is completely described in this article.
Abstract: The boundedness character of positive solutions of the following cyclic system of difference equationswhere A, p and q are positive numbers, and where if , for some and , then denotes , is completely described in this paper.
12 citations
TL;DR: Some sufficient conditions which guaranty the attractivity of all positive solutions of the next system of difference equations, where a, p > 0, and q j, j, are nonnegative numbers, are given.
12 citations
TL;DR: Global attractivity results on positive solutions of some special cases of the next max-type system of difference equations are presented.
7 citations
TL;DR: This work proves the existence of periodic solutions of a class of systems of differential-difference equations partially solved with respect to the first-order derivative by constructing it in a form of a series.
5 citations
TL;DR: Some sufficient conditions for the existence of an n-parameter family of solutions of a system of differential-difference equations converging to zero along with their first derivatives are given.
5 citations
TL;DR: Some results on the existence of bounded solutions together with their first derivatives of a class of neutral systems of functional differential equations with complicated deviations, which extend and unify numerous results in the literature are proved.
TL;DR: Some classes of systems of difference equations whose all well-defined solutions are periodic are presented in this paper, where the solution of each of them is a periodic system of difference equation.
Abstract: Some classes of systems of difference equations whose all well-defined solutions are periodic are presented in this note.
TL;DR: The characterizations for the Bloch space on the open unit disk in the complex plane were given in this paper, where the authors obtained some new characterizations of the ODE.
Abstract: We obtain some new characterizations for the Bloch space on the open unit disk in the complex plane ℂ and the open unit ball of . MSC:32A18.
TL;DR: This paper applies the part-metric method to study some types of higher-order symmetric difference equations with several different exponential parameters, proved to have unique equilibria and some useful inequalities regarding the difference equation functions are formulated.
TL;DR: Some sufficient conditions for the existence of families of bounded continuous solutions of some classes of systems of functional-difference equations on the intervals [0,+~] and (-~,0] are given.
TL;DR: Some sufficient conditions under which the zero solution of the next functional-differential equation x ′ ( t) is given, where a, b, c j, j = 1, k ‾ are real numbers and f : R l + 1 → R is a continuous function such that f = 0.
TL;DR: Some other properties related to solutions of the equation, as well as some properties of the solutions of an associate difference equation of first order are presented.
TL;DR: The asymptotic behavior and the existence of a bounded Lipschitz continuous solution of a system of nonlinear q-functional-difference equations on a half-interval of the real line are studied.
TL;DR: In this paper, it was shown that the limit ∞ ∞x(t) exists for every solution of the functional equation with bounded at infinity solution if and only if \({|\hat{a}|
eq 1}\).
Abstract: Let \({\mathbb{K} \in \{\mathbb{R}, \mathbb{C}\}, I = (d, \infty), \phi : I \to I}\) be unbounded continuous and increasing, X be a normed space over \({\mathbb{K}, \mathcal{F} : = \{f \in X^I : {\rm lim}_{t \to \infty} f(t) {\rm exists} \, {\rm in} X\},\hat{a} \in \mathbb{K}, \mathcal{A}(\hat{a}) : = \{\alpha \in \mathbb{K}^I : {\rm lim}_{t \to \infty} \alpha(t) = \hat{a}\},}\) and \({\mathcal{X} : = \{x \in X^I : {\rm lim} \, {\rm sup}_{t \to \infty} \|x(t)\| < \infty\}}\). We prove that the limit limt → ∞x(t) exists for every \({f \in \mathcal{F}, \alpha \in \mathcal{A}(\hat{a})}\) and every solution \({x \in \mathcal{X}}\) of the functional equation
$$x(\phi(t)) = \alpha(t) x(t) + f(t)$$
if and only if \({|\hat{a}|
eq 1}\). Using this result we study behaviour of bounded at infinity solutions of the functional equation
$$x(\phi^{[k]}(t)) = \sum_{j=0}^{k-1} \alpha_j(t) x (\phi^{[j]}(t)) + f(t),$$
under some conditions posed on functions \({\alpha_j(t), j = 0, 1,\ldots, k - 1,\phi}\) and f.