http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/847690.htmlWe use the theory of normal families to prove the following. Let Q1(z)=a1zp+a1,p−1zp−1+⋯+a1,0 and Q2(z)=a2zp+a2,p−1zp−1+⋯+a2,0 be two polynomials such that deg⁡Q1=deg⁡Q2=p (where p is a nonnegative integer) and a1,a2(a2≠0) are two distinct complex numbers. Let f(z) be a transcendental entire function. If f(z) and f′(z) share the polynomial Q1(z) CM and if f(z)=Q2(z) whenever f′(z)=Q2(z), then f≡f′. This result improves a result due to Li and Yi.Jianming Qi, Feng Lü, and Ang Chen© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/923476.htmlWe achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) for fixed integers a, b with a,b≠0 and a±b≠0.M. Eshaghi Gordji and H. Khodaei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/976369.htmlWe study the total stability in nonlinear discrete Volterra equations with unbounded delay, as a discrete analogue of the results for integrodifferential equations by Y. Hamaya (1990).Sung Kyu Choi, Yoon Hoe Goo, Dong Man Im, and Namjip Koo© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/438690.htmlThis paper is concerned with evolution equations of fractional order Dαu(t)=Au(t); u(0)=u0, u′(0)=0, where A is a differential operator corresponding to a coercive polynomial taking values in a sector of angle less than π and 1<α<2. We show that such equations are well posed in the sense that there always exists an α-times resolvent family for the operator A.Fu-Bo Li, Miao Li, and Quan Zheng© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/382574.htmlIn (2006) and (2009), Kim defined new generating functions of the Genocchi, Nörlund-type q-Euler polynomials and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type q-zeta function. This function interpolates Nörlund-type q-Euler polynomials at negative integers. We also give some identities related to these polynomials and functions. Furthermore, we give some remarks about approximations of Bernoulli and Euler polynomials.Mehmet Acikgoz and Yilmaz Simsek© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/617936.htmlThe boundedness of the motions of the dynamical system described by a differential inclusion with control vector is studied. It is assumed that the right-hand side of the differential inclusion is upper semicontinuous. Using positionally weakly invariant sets, sufficient conditions for boundedness of the motions of a dynamical system are given. These conditions have infinitesimal form and are expressed by the Hamiltonian of the dynamical system.Nihal Ege and Khalik G. Guseinov© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/246521.htmlThe boundedness and compactness of the extended Cesàro operator from logarithmic-type spaces to Bloch-type spaces on the unit ball are completely characterized in this paper.Dinggui Gu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/535678.htmlWe prove the generalized Hyers-Ulam stability of the following quadratic functional equations 2f((x+y)/2)+2f((x−y)/2)=f(x)+f(y) and f(ax+ay)+(ax−ay)=2a2f(x)+2a2f(y) in fuzzy Banach spaces for a nonzero real number a with a≠±1/2.Sun-Young Jang, Jung Rye Lee, Choonkil Park, and Dong Yun Shin© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/484158.htmlAll solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.Chengmin Hou and Sui Sun Cheng© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/512402.htmlBy using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an m-point singular p-Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (𝕋=ℝ) and difference equations (𝕋=ℤ), as well as in general time scales setting. As an application, an example is given to illustrate the results.Qiying Wei, You-Hui Su, Subei Li, and Xing-Xue Yan© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/187021.htmlA Chemostat system incorporating hepatocellular carcinomas is discussed. The model generalizes the classical Chemostat model, and it assumes that the Chemostat is an increasing function of the concentration. The asymptotic behavior of solutions is determined. Sufficient conditions for the local and global asymptotic stability of equilibrium and numerical simulation are obtained, which is used to select the disease control tactics.Qingyi Zhan, Xiangdong Xie, and Zhifang Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/562507.htmlWe provide a representation of elements of the space lp(A,X) for a locally convex space X and 1≤p<∞ and determine its continuous dual for normed space X and 1<p<∞. In particular, we study the extension and characterization of isometries on lp(N,X) space, when X is a normed space with an unconditional basis and with a symmetric norm. In addition, we give a simple proof of the main result of G. Ding (2002).Xiaohong Fu and Songxiao Li© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/612392.htmlIn 2006, C. Park proved the stability of homomorphisms in C∗-ternary algebras and of derivations on C∗-ternary algebras for the following generalized Cauchy-Jensen additive mapping: 2f((∑j=1pxj/2)+∑j=1dyj)=∑j=1pf(xj)+2∑j=1df(yj). In this note, we improve and generalize some results concerning this functional equation.Abbas Najati, Choonkil Park, and Jung Rye Lee© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/573156.htmlWe propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.Jong Soo Jung© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/987343.htmlWe obtain sufficient conditions which guarantee the global attractivity of solutions for nonlinear delay survival red blood cells model. Then, some criteria are established for the existence, uniqueness and global attractivity of positive almost periodic solutions of the almost periodic system.Xitao Yang and Siping Tang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/301967.htmlA new 4-point C3 quaternary approximating subdivision scheme with one shape parameter is proposed and analyzed. Its smoothness and approximation order are higher but support is smaller in comparison with the existing binary and ternary 4-point subdivision schemes.Ghulam Mustafa and Faheem Khan© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/974394.htmlBased on the Gateaux differential on time scales, we investigate and establish necessary conditions for Lagrange optimal control problems on time scales. Moreover, we present an economic model to demonstrate the effectiveness of our results.Zaidong Zhan and W. Wei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/280790.htmlWe consider the one-dimensional viscoelastic Porous-Thermo-Elastic system. We establish a general decay results. The usual exponential and polynomial decay rates are only special cases.Abdelaziz Soufyane, Mounir Afilal, and Mama Chacha© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/152964.htmlWe study global behavior of the following max-type difference equation xn+1=max⁡{1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf⁡An≤sup⁡An<1. The special case when {An}n=0∞ is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case.Taixiang Sun, Bin Qin, Hongjian Xi, and Caihong Han© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/216746.htmlThis paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. Both differential equations involve point and distributed delayed dynamics including Volterra class dynamics. The proofs are based on a Perron-type theorem for functional equations so that the comparison is governed by the real part of a dominant zero of the characteristic equation of the nominal differential equation. The obtained results are also applied to investigate the global stability of the perturbed equation based on that of its corresponding limiting equation.M. De la Sen© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/360794.htmlIn the theorems of Galambos-Bojanić-Seneta's type, the asymptotic behavior of the functions c[x],  x≥1, for x→+∞, is investigated by the asymptotic behavior of the given sequence of positive numbers (cn), as n→+∞ and vice versa. The main result of this paper is one theorem of such a type for sequences of positive numbers (cn) which satisfy an asymptotic condition of the Karamata type lim¯n→∞ c[λn]/cn>1, for λ>1.Dragan Djurčić and Aleksandar Torgašev© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/363927.htmlThis paper is devoted to studying growth of solutions of linear differential equations of type f(k)+Ak−1(z)f(k−1)+⋯+A1(z)f′+A0(z)f=H(z) where Aj (j=0,…,k−1) and H are entire functions of finite order.Jun Wang and Ilpo Laine© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/161528.htmlHere we introduce the nth weighted space on the upper half-plane Π+={z∈ℂ:Im z>0} in the complex plane ℂ. For the case n=2, we call it the Zygmund-type space, and denote it by 𝒵(Π+). The main result of the paper gives some necessary and sufficient conditions for the boundedness of the composition operator Cφf(z)=f(φ(z)) from the Hardy space Hp(Π+) on the upper half-plane, to the Zygmund-type space, where φ is an analytic self-map of the upper half-plane.Stevo Stević© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/290978.htmlLet H(B) denote the space of all holomorphic functions on the unit ball B. Let u∈H(B) and φ be a holomorphic self-map of B. In this paper, we investigate the boundedness and compactness of the weighted composition operator uCφ from the general function space F(p,q,s) to the weighted-type space Hμ∞ in the unit ball.Xiangling Zhu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/639439.htmlBy using the ordinary fermionic p-adic invariant integral on ℤp, we derive some interesting identities related to the Frobenius-Euler polynomials.Taekyun Kim and Byungje Lee© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/603591.htmlThe paper is concerned with a two-dimensional Landau-Lifshitz equation which was first raised by A. DeSimone and F. Otto, and so fourth, when studying thin film micromagnetics. We get the existence of a local weak solution by approximating it with a higher-order equation. Penalty approximation and semigroup theory are employed to deal with the higher-order equation.Jingna Li© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/360432.htmlUsing fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in C∗-algebras and Lie C∗-algebras and also of derivations on C∗-algebras and Lie C∗-algebras for the Jensen-type functional equation f((x+y)/2)+f((x−y)/2)=f(x).Choonkil Park and John Michael Rassias© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2009/350762.htmlWe construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are described as well. In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.V. G. Danilov and D. Mitrovic© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2008/636843.htmlThe nonmonotonic differentiable solutions of equations involving iterated functional series are investigated. Conditions for the existence, uniqueness, and stability of such solutions are given. These extend earlier results due to Murugan and Subrahmanyam.Wei Song© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2008/893409.htmlWe work on RD-spaces 𝒳, namely, spaces of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝒳. An important example is the Carnot-Carathéodory space with doubling measure. By constructing an approximation of the identity with bounded support of Coifman type, we develop a theory of Besov and Triebel-Lizorkin spaces on the underlying spaces. In particular, this includes a theory of Hardy spaces Hp(𝒳) and local Hardy spaces hp(𝒳) on RD-spaces, which appears to be new in this setting. Among other things, we give frame characterization of these function spaces, study interpolation of such spaces by the real method, and determine their dual spaces when p≥1. The relations among homogeneous Besov spaces and Triebel-Lizorkin spaces, inhomogeneous Besov spaces and Triebel-Lizorkin spaces, Hardy spaces, and BMO are also presented. Moreover, we prove boundedness results on these Besov and Triebel-Lizorkin spaces for classes of singular integral operators, which include non-isotropic smoothing operators of order zero in the sense of Nagel and Stein that appear in estimates for solutions of the Kohn-Laplacian on certain classes of model domains in ℂN. Our theory applies in a wide range of settings.Yongsheng Han, Detlef Müller, and Dachun Yang© 2009, Hindawi Publishing Corporation. All rights reserved.