جستجوی مقالات مرتبط با کلیدواژه "boundedness" در نشریات گروه "ریاضی"

Let $\mathbb{D}= \{\upsilon\in\mathbb{C}:|\upsilon|<1\}$ be the open unit disk in the complex plane $\mathbb{C}$ and let $H(\mathbb{D})$ be the space of all holomorphic functions on  $\mathbb{D}$. For a non-negative integer $n$ and a function $f \in H(\mathbb{D})$, the $n^{th}-$ order differentiation operator is defined as $D^n f = f^{(n)}$. The weighted composition operator together with $n^{th}-$ order differentiation operator give rise to a new operator generally termed as generalized weighted composition operator denoted by $\mathcal{W}^{n}_{\phi,\xi}$ and is  defined by\begin{equation*}\mathcal{W}^{n}_{\phi,\xi}f(\upsilon)  =\phi(\upsilon)f^{(n)}(\xi(\upsilon)),\quad f\in H(\mathbb{D}); \upsilon\in%\mathbb{D},\end{equation*}where $\phi\in H(\mathbb{D})$ and $\xi$ is a holomorphic self-map of $\mathbb{D}$. This operator is basically the combination of multiplication operator $M_{\phi}$, composition operator  $C_{\xi}$ and $n^{th}-$ order differentiation operator $D^{n}$. We study the boundedness and compactness of this operator between Dirichlet-type spaces and Bloch-type spaces.

In this paper,  we characterize the boundedness and compactness of product type operators, including Stevi\'c-Sharma operator $T_{\nu_1,\nu2,\varphi}$,  from weak vector valued derivative Besov space $w\mathcal{E}^p_\beta(X)$ into weak vector-valued Besov space $w\mathcal{B}^p_\beta(X)$. As an application, we obtain the boundedness and compactness characterizations of the weighted composition operator on the weak vector valued derivative  Besov space.

This paper deals with a class of stochastic delay differential equations (SDDEs) of second order with multiple delays. Here, two main and novel results are proved on stochastic asymptotic stability and stochastic boundedness of solutions of the considered SDDEs. In the proofs of results, the Lyapunov-Krasovskii functional (LKF) method is used as the main tool. A comparison between our results and those are available in the literature shows that the main results of this paper have new contributions to the related ones in the current literature. Two numerical examples are given to show the applications of the given results.

In this paper, we investigate the global behavior of positive solutions of the system of difference equations \begin{equation*} x_{n+1}=\alpha+ \dfrac{y^p_{n}}{y^p_{n-2}},\y_{n+1}=\alpha+ \dfrac{x^q_{n} }{x^q_{n-2}},\ n=0, 1, 2, ...\end{equation*}where parameters $\alpha, p, q \in (0, \infty)$ and the initial values $x_{i}$, $y_{i}$ are arbitrary positive numbers for $ i= -2,-1, 0$. Moreover, the rate of convergence of positive solutions is established and some numerical examples are given to demonstrate our theoretical results.

This paper establishes sufficient conditions to ensure the stability and boundedness of zero solution and square integrability of solutions and their derivatives to neutral-type nonlinear differential equations of fourth order by constructing Lyapunov functionals.

In this work, we study a data visualization problem which is classified in the field of shape-preserving interpolation. When   function  is known to be bounded, then it is  natural to expect its interpolant to adhere boundedness. Two spline-based techniques are proposed to handle this kind of problem. The proposed methods   use quadratic splines as basis and involve solving a linear programming or a mixed integer linear  programming problem which gives $C^1$ interpolants. An energy minimization technique is employed to gain the optimal smooth solution. The reliability  and  applicability of  the proposed techniques  have been illustrated through examples.

A class of Bernstein-like basis functions, equipped with a shape param-eter, is presented. Employing the introduced basis functions, the corre-sponding curve and surface in rectangular patches are defined based on some control points. It is verified that the new curve and surface have most properties of the classical Bézier curves and surfaces. The shape parameter helps to adjust the shape of the curve and surface while the control points are fixed. We prove that the proposed Bézier-like curves can preserve monotonicity and that Bézier-like surfaces can preserve axial monotonicity. Moreover, the presented curves and surfaces preserve bound constraints implied by the original data.

Let Hμ=(μn+k)n,k≥0 with entries μn,k=μn+k induces the operator Hμ(f)(z)=∑∞n=0(∑∞k=0μn,kak)zn on the space of all analytic functions f(z)=∑∞n=0anzn in the unit disk D, where μ is a positive Borel measure on the interval [0,1). In this paper, we characterize the boundedness and compactness of the operator Hμ on Zygmund type spaces.

This work deals with various qualitative analyses of solutions of a certain delay integro-differential equation (DIDE). We prove here six new theorems including sufficient conditions, on uniformly stability (US), boundedness, asymptotically stability (AS), exponentially stability (ES), integrability and instability of solutions, respectively. By defining a suitable Lyapunov function (LF) and using the Razumikhin method (RM), the proofs of the theorems are provided. We gave two examples to demonstrate applications of the established new conditions.

The aim of this paper is to study the dynamics of the system of two rational difference equations: xn+1=αn+yn−kyn,yn+1=αn+xn−kxn,n=0,1,… where {αn}n≥0 is a two periodic sequence of nonnegative real numbers and the initial conditions xi,yi are arbitrary positive numbers for i=−k,−k+1,−k+2,…,0 and k∈N. We investigate the boundedness character of positive solutions. In addition, we establish some sufficient conditions under which the local asymptotic stability and the global asymptotic stability are assured. Furthermore, we determine the rate of the convergence of the solutions. Some numerical are considered in order to confirm our theoretical results.

For an analytic self-map ‎$‎‎varphi‎$ ‎of ‎the ‎unit disk ‎‎$‎‎mathbb{D}‎$ ‎in ‎the ‎complex ‎plane $‎‎mathbb{C}‎‎$‎,‎ a nonnegative integer ‎$‎n‎$‎, and ‎$u‎$ ‎analytic function ‎on ‎‎$‎‎mathbb{D}‎‎$‎, weighted differentiation composition operator is defined by ‎$(D_{varphi,u}^nf) (z)=u(z)f^{(n)}(varphi(z))$‎‎, where ‎$‎f‎$ is an ‎analytic function ‎on‎ ‎‎$‎‎mathbb{D}‎$ and ‎$‎zinmathbb{D}‎$‎.‎ In this paper, we study the boundedness‎ and compactness of ‎ $D_{varphi,u}^n‎$, ‎‎ ‎from weighted Bergman spaces with admissible ‎weights‎ to Bloch-type spaces.

In this paper we study the weighted composition operator ψCφ on the Dirichlet type spaces Dp α(D). We show that if the weighted composition operator ψCφ is bounded on such spaces(for 1  p < 2) then the related measure µp,α,ψ is a Carleson measure. Also we show that if the weighted composition operator ψCφ is an isomety on Dp α(D) then ψ.φ is a rotation map on D.

In this paper, an explicit exact finite-difference scheme for the Huxley equation is presented based on the nonstandard finite-difference (NSFD) scheme. Afterwards, an NSFD scheme is proposed for the numerical solution of the Huxley equation. The positivity and boundedness of the scheme is discussed. It is shown through analysis that the proposed scheme is consistent, stable, and convergence. The numerical results obtained by the NSFD scheme is compared with the exact solution and some available methods, to verify the accuracy and efficiency of the NSFD scheme.

In this paper, an economic group delay model is established. Dynamical behavior and Basic influence number of the proposed system are studied. Asymptotic stability analysis is carried out for the steady-states. The critical value of the delay $tau$ is determined. It is observed that for the interior steady-state remains stable if the adoption delay for the low-income group is less than the threshold value, i.e., $tau<tau_{0}^+$. If $tau$ crosses its threshold, system perceives oscillating behavior, and Hopf bifurcation occurs. Moreover, sensitivity analysis is performed for the system parameter used in the interior steady-state. Finally, numerical simulations are conducted to support our analytical findings.

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= \beta x_n(1- x_n),\ \ n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $\beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Hukuhara difference for fuzzy numbers. Finally, some examples are given to illustrate our results.

Abstract. In the present paper a generalized Lotka-Volterra food chain system has been studied and also its dynamic behavior such as locally asymptotic stability has been analyzed in case of existing interspecies competition. Furthermore, it has been shown that the said system is permanent (in the sense of boundedness and uniformly persistent). Finally, it is proved that the nontrivial equilibrium point of the above system is locally asymptotically stable.

We investigate the long-term behavior of solutions of the di erence equation x_n+1 = x_nx_n-3 - 1; n = 0; 1; :: :; where the initial conditions x-3; x-2; x-1; x0 are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

We consider the bilinear Fourier integral operator S(f, g)(x) = Z Rd Z Rd ei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d, on modulation spaces. Our aim is to indicate this operator is well defined on S(Rd) and shall show the relationship between the bilinear operator and BFIO on modulation spaces.