Issue 2, Volume 39, June 2014

2014

1. Qualitative behavior of difference equation of order two and positive nonoscillatory solutions Khuong Vu Van , Thai Tran Hong PDF

   ▸ Abstract

   In the paper we deal with the qualitative behavior of solutions of the following equation: $$x_{n+1}=ax_{n-1}-\dfrac{bx_n^2+cx_{n-1}^2}{1-dx_n+ex_{n-1}},\quad n=0,1,2,\dots$$ where the initial values $x_{−1},x 0$ are arbitrary positive numbers and $a,b,c,d,e$ are positive numbers. We also study the positive nonoscillatory solutions of the difference equation $$x_{n+1}=ax_{n-1}-\dfrac{bx_n^2+ax_{n-1}^2}{1-cx_n+x_{n-1}},\quad n=0,1,2,\dots.$$

   111-119
2. Global Existence and Decay Rates of Solutions of Generalized Benjamin–Bona–Mahony Equations in Multiple Dimensions Hongmei Xu , Guyu Xin PDF

   ▸ Abstract

   We study the global existence and decay rates of the Cauchy problem for the generalized Benjamin–Bona–Mahony equations in multi-dimensional spaces. By using Fourier analysis, frequency decomposition, pseudo-differential operators and the energy method, we obtain global existence and optimal $L_2$ convergence rates of the solution.

   121-131
3. Asymptotic stability and regularity of solutions for a magnetoelastic system in bounded domains J. C. Oliveira PDF

   ▸ Abstract

   We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as $t\to \infty$ for a semilinear (nonlinearly coupled) magnetoelastic system in bounded, simply connected three-dimensional domain. The mathematical model includes a mechanical dissipation and a periodic forcing function of period $T$. In the second part of the paper, we consider a magnetoelastic system in the form of a semilinear initial-boundary-value problem in a bounded, simply connected two-dimensional domain. We use the LaSalle invariance principle to obtain results on the asymptotic behavior of solutions. This second result was obtained for the system under the action of only one dissipation (the natural dissipation of the system).

   133-150
4. Global attractivity of almost periodic solutions for competitive Lotka–Volterra diffusion system Ahmadjan Muhammadhaji, Zhidong Teng, Mehbuba Rehim PDF

   ▸ Abstract

   In this paper, two competitive Lotka–Volterra populations in the two-patch-system with diffusion are considered. Each of the two species can diffuse independently and discretely between its intrapatch and interpatch. By means of a Lyapunov function, under a moderate condition, the system has a unique almost periodic solution, which is asymptotically stable and globally attractive.

   151-161
5. Some results on random coincidence points of completely random operators Dang Hung Thang , Pham The Anh PDF

   ▸ Abstract

   The purpose of this paper is to examine the notion of completely random operators and to present some results on the existence of random coincidence points of completely random operators. Some applications to random fixed point theorems and random equations are given.

   163-184
6. Fekete–Szegö problem for certain classes of analytic functions of complex order defined by the Dziok–Srivastava operator Tariq Al-Hawary , B. A. Frasin , M. Darus PDF

   ▸ Abstract

   By using the hypergeometric function defined by the Dziok–Srivastava operator, new subclasses of analytic functions are introduced. For these classes, the Fekete–Szegö problem is obtained. Various known or new special cases of our results are pointed out.

   185-192
7. On approximation of certain integral operators Vijay Gupta , Rani Yadav PDF

   ▸ Abstract

   In the present paper we introduce the summation-integral type modified Lupas operators with weights of Beta basis functions. We define the operators in terms of hypergeometric series and, using such an approach, establish moments. Our main results are an asymptotic formula and an error estimate in terms of modulus of continuity and weighted approximation and rate of convergence for functions having bounded derivatives.

   193-203
8. On the derived functors of destabilization at odd primes Geoffrey M. L. Powell PDF

   ▸ Abstract

   An explicit chain complex is constructed to calculate the derived functors of destabilization at an odd prime, generalizing constructions of Zarati and of Hung and Sum. The methods are based on the ideas of Singer and Miller and also apply at the prime two. A structural result on the derived functors of destabilization is deduced.

   205-236
9. Well-posedness of the ADMB–KdV equation in Sobolev spaces of negative indices Amin Esfahani , Reza Pourgholi PDF

   ▸ Abstract

   In this paper, we study the ADMB–KdV equation. We show that the associated initial value problem is locally well posed in Sobolev spaces $H^s(\mathbb R^2)$ for $s > −1/2$. We also prove that our result is sharp in some sense.

   237-251
10. Weak convergence theorems for strongly continuous semigroups of pseudocontractions Duong Viet Thong PDF

    ▸ Abstract

    Let $K$ be a nonempty closed convex subset of a uniformly convex Banach space E, let $\{T(t) : t \geq 0\}$ be a strongly continuous semigroup of nonexpansive mappings from $K$ into itself such that $F := \cap_{T\geq 0} F(T (t)) \not=\emptyset$. Assuming that $\{\alpha_n\}$ and $\{t_n\}$ are sequences of real numbers satisfying appropriate conditions, we show that the sequence $x_n$ defined by $$x_n=\alpha_nx_{n-1}+(1-\alpha_n)T(t_n)x_n$$ converges weakly to an element of $F$. This extends Thong’s result (Thong, Nonlinear Anal. 74, 6116–6120, 2011) from a Hilbert space setting to a Banach space setting. Next, theorems of weak convergence of an implicit iterative algorithm with errors for treating a strongly continuous semigroup of Lipschitz pseudocontractions are established in the framework of a real Banach space.

    253-261
11. On a generalized convolution with a weight-function for the Hartley and Fourier cosine transforms Nguyen Minh Khoa PDF

    ▸ Abstract

    In this paper, we introduce a generalized convolution with a weight-function for the Hartley and Fourier cosine transforms. Several algebraic properties and applications of this generalized convolution to solving a class of integral equations of Toeplitz plus Hankel type and a class of systems of integral equations are presented.

    263-276