http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/aaa/2012/548612/Compact subsets of a topological space are used to define coc-open sets as new generalized open sets, and then coc-open sets are used to define (coc)∗-open sets as another type of generalized open sets. Several results and examples related to them are obtained; particularly a decomposition of open sets is given. Also, coc-open sets and (coc)∗-open sets are used to introduce coc-continuity and (coc)∗-continuity, respectively. As a main result, a decomposition theorem of continuity is obtained.Samer Al Ghour and Salti SamarahCopyright © 2012 Samer Al Ghour and Salti Samarah. All rights reserved.http://www.hindawi.com/journals/aaa/2012/530209/We consider the existence of the periodic solutions in the neighbourhood of equilibria for C∞ equivariant Hamiltonian vector fields. If the equivariant symmetry S acts antisymplectically and S2=I, we prove that generically purely imaginary eigenvalues are doubly degenerate and the equilibrium is contained in a local two-dimensional flow-invariant manifold, consisting of a one-parameter family of symmetric periodic solutions and two two-dimensional flow-invariant manifolds each containing a one-parameter family of nonsymmetric periodic solutions. The result is a version of Liapunov Center theorem for a class of equivariant Hamiltonian systems.Jia Li and Yanling ShiCopyright © 2012 Jia Li and Yanling Shi. All rights reserved.http://www.hindawi.com/journals/aaa/2012/125987/We study multiplicative isometries on the following F-algebras of holomorphic functions: Smirnov class N*(X), Privalov class Np(X), Bergman-Privalov class ANαp(X), and Zygmund F-algebra NlogβN(X), where X is the open unit ball 𝔹n or the open unit polydisk 𝔻n in ℂn.Osamu Hatori, Yasuo Iida, Stevo Stević, and Sei-Ichiro UekiCopyright © 2012 Osamu Hatori et al. All rights reserved.http://www.hindawi.com/journals/aaa/2012/582854/Let F be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer. Suppose that, for every function f∈F, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0 and, for every pair functions (f,g)∈F, P(f), P(g) share ψ, then F is normal in D.Jie Ding, Jianming Qi, and Taiying ZhuCopyright © 2012 Jie Ding et al. All rights reserved.http://www.hindawi.com/journals/aaa/2012/952052/It is shown that occasionally JH operators as well as occasionally weakly biased mappings reduce to weakly compatible mappings in the presence of a unique point of coincidence (and a unique common fixed point) of the given maps.Mohammad Ali Alghamdi, Stojan Radenović, and Naseer ShahzadCopyright © 2012 Mohammad Ali Alghamdi et al. All rights reserved.http://www.hindawi.com/journals/aaa/2012/530468/We firstly construct a concrete semi-invex set which is not invex. Basing on concept of semi-invex set, we introduce some kinds of generalized convex functions, which include semi-(B,G)-preinvex functions, strictly semi-(B,G)-preinvex functions and explicitly semi-(B,G)-preinvex functions. Moreover, we establish relationships between our new generalized convexity and generalized convexity introduced in the literature. With these relationships and the well-known results pertaining to common generalized convexity, we obtain results for our new generalized convexities. We extend the existing results in the literature.Xiaoling Liu and D. H. YuanCopyright © 2012 Xiaoling Liu and D. H. Yuan. All rights reserved.http://www.hindawi.com/journals/aaa/2012/795304/The purpose of this paper is to investigate some properties of q-Euler numbers and polynomials with weight 0. From those q-Euler numbers with weight 0, we derive some identities on the q-Euler numbers and polynomials with weight 0.T. Kim and J. ChoiCopyright © 2012 T. Kim and J. Choi. All rights reserved.http://www.hindawi.com/journals/aaa/2012/649517/The present paper deles with a fractional differential equation zαDzαu(z)+zu'(z)+(z2-a2)u(z)=∑n=0∞anzn+α, 1<α≤2, where z∈U:={z:|z|<1} in sense of Srivastava-Owa fractional operators. The existence and uniqueness of holomorphic solutions are established. Ulam stability for the approximation and holomorphic solutions are suggested.Rabha W. IbrahimCopyright © 2012 Rabha W. Ibrahim. All rights reserved.http://www.hindawi.com/journals/aaa/2012/653508/Badora (2002) proved the following stability result. Let ε and δ be nonnegative real numbers, then for every mapping f of a ring R onto a Banach algebra B satisfying ||f(x+y)-f(x)-f(y)||≤ε and ||f(x⋅y)-f(x)f(y)||≤δ for all x,y∈R, there exists a unique ring homomorphism h:R→B such that ||f(x)-h(x)||≤ε, x∈R. Moreover, b⋅(f(x)-h(x))=0, (f(x)-h(x))⋅b=0, for all x∈R and all b from the algebra generated by h(R). In this paper, we generalize Badora's stability result above on ring homomorphisms for Riesz algebras with extended norms.Faruk PolatCopyright © 2012 Faruk Polat. All rights reserved.http://www.hindawi.com/journals/aaa/2012/285807/We establish some stability results over p-adic fields for the generalized quadratic functional equation ∑k=2n∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir)+f(∑i=1nxi)=2n-1∑i=1nf(xi), where n∈N and n≥2.M. Eshaghi Gordji, H. Khodaei, and Gwang Hui KimCopyright © 2012 M. Eshaghi Gordji et al. All rights reserved.http://www.hindawi.com/journals/aaa/2012/804942/We first present two convergence results about the second-order quadratic variations of the subfractional Brownian motion: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we combine these results and concentration inequalities to build confidence intervals for the self-similarity parameter associated with one-dimensional subfractional Brownian motion.Junfeng Liu, Litan Yan, Zhihang Peng, and Deqing WangCopyright © 2012 Junfeng Liu et al. All rights reserved.http://www.hindawi.com/journals/aaa/2012/580750/The paper investigates a dynamic equation Δy(tn)=β(tn)[y(tn−j)−y(tn−k)] for n→∞, where k and j are integers such that k>j≥0, on an arbitrary discrete time scale T:={tn} with tn∈ℝ, n∈ℤn0−k∞={n0−k,n0−k+1,…}, n0∈ℕ, tn<tn+1, Δy(tn)=y(tn+1)−y(tn), and limn→∞tn=∞. We assume β:T→(0,∞). It is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent for n→∞. The results are presented as inequalities for the function β. Examples demonstrate that the criteria obtained are sharp in a sense.J. Diblík, M. Růžičková, Z. Šmarda, and Z. ŠutáCopyright © 2012 J. Diblík et al. All rights reserved.http://www.hindawi.com/journals/aaa/2012/569201/The purpose of this paper is to examine oscillatory properties of the third-order neutral delay differential equation [a(t)(b(t)(x(t)+p(t)x(σ(t)))′)′]′+q(t)x(τ(t))=0. Some oscillatory and asymptotic criteria are presented. These criteria improve and complement those results in the literature. Moreover, some examples are given to illustrate the main results.Tongxing Li, Chenghui Zhang, and Guojing XingCopyright © 2012 Tongxing Li et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/432963/Some new properties are obtained for generalized second-order contingent (adjacent) epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.Qilin Wang and Guolin YuCopyright © 2011 Qilin Wang and Guolin Yu. All rights reserved.http://www.hindawi.com/journals/aaa/2011/630583/A rate of complete convergence for weighted sums of arrays of rowwise independent random variables was obtained by Sung and Volodin (2011). In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences of φ-mixing and ρ*-mixing random variables are also obtained. Our results improve and generalize the results of Baek et al. (2008), Kuczmaszewska (2009), and Wang et al. (2010).Soo Hak SungCopyright © 2011 Soo Hak Sung. All rights reserved.http://www.hindawi.com/journals/aaa/2011/712746/The theory of the diffraction Fresnel transform is extended to certain spaces of Schwartz distributions. In the context of Boehmian spaces, the diffraction Fresnel transform is obtained as a continuous function. Convergence with respect to δ and Δ is also defined.S. K. Q. Al-Omari and A. KılıçmanCopyright © 2011 S. K. Q. Al-Omari and A. Kılıçman. All rights reserved.http://www.hindawi.com/journals/aaa/2011/714728/By using fixed-point theorems of a cone, we investigate the existence and multiplicity of positive solutions for complementary Lidstone boundary value problems: -1nu2n+1t=htf(u(t)), in 0<t<1, u0=0, u2i+10=u2i+11=0, 0≤i≤n-1, where n∈N.Fanglei Wang and Yukun AnCopyright © 2011 Fanglei Wang and Yukun An. All rights reserved.http://www.hindawi.com/journals/aaa/2011/634675/The purpose of this paper is to give some properties of several q-Bernstein-type polynomials to express the q-integral on [0, 1] in terms of q-beta and q-gamma functions. Finally, we derive some identities on the q-integral of the product of several q-Bernstein-type polynomials.Taekyun KimCopyright © 2011 Taekyun Kim. All rights reserved.http://www.hindawi.com/journals/aaa/2011/902131/New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence {xk} generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of {xk} is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally.Jinchuan Zhou, Xunzhi Zhu, Lili Pan, and Wenling ZhaoCopyright © 2011 Jinchuan Zhou et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/328914/This paper studies the second-order nonlinear neutral delay difference equation Δ[anΔ(xn+bnxn−τ)+f(n,xf1n,…,xfkn)]+g(n,xg1n,…,xgkn)=cn, n≥n0. By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence results of uncountably many bounded nonoscillatory, positive, and negative solutions for the equation, respectively. Ten examples are given to illustrate the results presented in this paper.Zeqing Liu, Liangshi Zhao, Jeong Sheok Ume, and Shin Min KangCopyright © 2011 Zeqing Liu et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/207930/The Sumudu transform of certain elementary matrix functions is obtained. These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.Hassan Eltayeb, Adem Kılıçman, and Ravi P. AgarwalCopyright © 2011 Hassan Eltayeb et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/986738/The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.Luisa Malaguti, Cristina Marcelli, and Serena MatucciCopyright © 2011 Luisa Malaguti et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/375897/We derive several subordination results for a certain class of analytic functions defined by the Sălăgean operator In the present investigation.S. Sivasubramanian, Aabed Mohammed, and Maslina DarusCopyright © 2011 S. Sivasubramanian et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/518972/Firstly, an inequality for vector-valued meromorphic functions is established which extend a corresponding inequality of Milloux for meromorphic scalar-valued function (1946). As an application, the relationship between the characteristic function of a vector-valued meromorphic function f and its derivative f' is studied, results are obtained to extend some related results for meromorphic scalar-valued function of Weitsman (1969) and Singh and Gopalakrishna (1971).Wu Zhaojun and Chen YuxianCopyright © 2011 Wu Zhaojun and Chen Yuxian. All rights reserved.http://www.hindawi.com/journals/aaa/2011/671765/We present some monotonicity, convexity, and inequalities for the Agard distortion function ηK(t) and improve some well-known results.Yu-Ming Chu, Miao-Kun Wang, Yue-Ping Jiang, and Song-Liang QiuCopyright © 2011 Yu-Ming Chu et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/420419/We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.Agata Caserta, Giuseppe Di Maio, and Ljubiša D. R. KočinacCopyright © 2011 Agata Caserta et al. All rights reserved.http://www.hindawi.com/journals/aaa/2011/903736/The main purpose of this paper is considering the lacunary sequence spaces defined by Karakaya (2007), by proving the property (β) and Uniform Opial property.Chirasak Mongkolkeha and Poom KumamCopyright © 2011 Chirasak Mongkolkeha and Poom Kumam. All rights reserved.http://www.hindawi.com/journals/aaa/2011/502903/We consider the following additive functional equation with n-independent variables: f(∑i=1nxi)=∑i=1nf(xi)+∑i=1nf(xi-xi-1) in the spaces of generalized functions. Making use of the heat kernels, we solve the general solutions and the stability problems of the above equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the mollifiers, we extend these results to the space of distributions.Young-Su LeeCopyright © 2011 Young-Su Lee. All rights reserved.http://www.hindawi.com/journals/aaa/2011/503679/We show that the following K0-monoid properties of C*-algebras in the class Ω are inherited by simple unital C*-algebras in the class TAΩ: (1) pseudocancellation property, (2) weakly divisible, (3) strongly separative, (4) separative, and (5) preminimal.Qingzhai FanCopyright © 2011 Qingzhai Fan. All rights reserved.http://www.hindawi.com/journals/aaa/2011/142128/We investigate the asymptotic behavior of scalar diffusion equation with small time delay ut-Δu=f(ut,u(t-τ)). Roughly speaking, any bounded solution will enter and stay in the neighborhood of one equilibrium when the equilibria are discrete.Xunwu YinCopyright © 2011 Xunwu Yin. All rights reserved.