http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/962849We introduce a q-analogues of Wright function and its auxiliary functions as Barnes integral representations and series expansion. The relations between q-analogues of Wright function and some other functions are investigated.Moustafa El-Shahed and Ahmed Salem© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/232187The main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. Finally, we derive the following interesting formula: Gn+k,q(k)(x)=2kk!(n+kk)∑l=0∞∑d0+d1+⋯+dk=k−1,di∈ℕ(−1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k.Leechae Jang and Taekyun Kim© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/581582For s∈ℂ, the Euler zeta function and the Hurwitz-type Euler zeta function are defined by ζE(s)=2∑n=1∞((−1)n/ns), and ζE(s,x)=2∑n=0∞((−1)n/(n+x)s). Thus, we note that the Euler zeta functions are entire functions in whole complex s-plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers. That is, ζE(−k)=Ek∗, and ζE(−k,x)=Ek∗(x). We give some interesting identities between the Euler numbers and the zeta functions. Finally, we will give the new values of the Euler zeta function at positive even integers.Taekyun Kim© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/439781Commutative symmetric operator families of the so-called D_+-class are considered in Krein spaces. It is proved that the restriction of a family of this type on a special kind of invariant subspace is similar to a family of operators adjoint to multiplication operators by scalar functions acting on a suitable function space.Vladimir Strauss© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/184243We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regular-Lindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish some of their relations.Adem Kılıçman and Zabidin Salleh© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/915292We need to take account of the superstability for generalized left derivations (resp., generalized derivations) associated with a Jensen-type functional equation, and we also deal with problems for the Jacobson radical ranges of left derivations (resp., derivations).Sheon-Young Kang and Ick-Soon Chang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/135237We obtain the general solution and the stability of the functional equation f(x+y+z,u+v+w)+f(x+y−z,u+v+w)+2f(x,u−w)+2f(y,v−w)=f(x+y,u+w)+f(x+y,v+w)+f(x+z,u+w)+f(x−z,u+v−w)+f(y+z,v+w)+f(y−z,u+v−w). The function f(x,y)=x3+ax+b−y2 having level curves as elliptic curves is a solution of the above functional equation.Won-Gil Park and Jae-Hyeong Bae© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/485706A function f is continuous if and only if, for each point x0 in the domain, lim⁡n→∞f(xn)=f(x0), whenever lim⁡n→∞xn=x0. This is equivalent to the statement that (f(xn)) is a convergent sequence whenever (xn) is convergent. The concept of slowly oscillating continuity is defined in the sense that a function f is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, (f(xn)) is slowly oscillating whenever (xn) is slowly oscillating. A sequence (xn) of points in R is slowly oscillating if limλ→1+lim―nmaxn+1≤k≤[λn]|xk-xn|=0, where [λn] denotes the integer part of λn. Using ɛ>0's and δ's, this is equivalent to the case when, for any given ɛ>0, there exist δ=δ(ɛ)>0 and N=N(ɛ) such that |xm−xn|<ɛ if n≥N(ɛ) and n≤m≤(1+δ)n. A new type compactness is also defined and some new results related to compactness are obtained.H. Çakalli© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/178534We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.M. E. Amendola, L. Rossi, and A. Vitolo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/498173We give the twisted Carlitz's type q-Bernoulli polynomials and numbers associated with p-adic q-inetgrals and discuss their properties. Furthermore, we define the multiple twisted Carlitz's type q-Bernoulli polynomials and numbers and obtain the distribution relation for them.Lee-Chae Jang and Cheon-Seoung Ryoo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/836124For a certain range of the value p in the nonlinear term |u|pu, in this paper we mainly study the global existence and uniqueness of global self-similar solutions to the Cauchy problem for some nonlinear Schrödinger equations using the method of harmonic analysis.Yaojun YE© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/196498We estimate the essential norm of a compact weighted composition operator uCφ acting between different Hardy spaces of the unit ball in ℂN. Also we will discuss a compact multiplication operator between Hardy spaces.Sei-Ichiro Ueki and Luo Luo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/374742Let (Ω,𝒜,μ) be a probability space and ℒ⊂𝒜 a sub-σ-lattice of the σ-algebra 𝒜. We study an extension of the best ϕ-approximation operator from an Orlicz space Lϕ to the space Lϕ′, where ϕ′ denotes the derivative of the convex, but not necessarily a strictly convex function ϕ. We obtain convergence results when a sequence of σ-algebras ℬn converges to ℬ∞ in a suitable way.Ivana Carrizo, Sergio Favier, and Felipe Zó© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/628178Let X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx+y)+f(kx-y)=2k2f(x)+2f(y) for all x,y∈X if and only if the mapping f:X→Y satisfies f(x+y)+f(x-y)=2f(x)+2f(y) for all x,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.Jung Rye Lee, Jong Su An, and Choonkil Park© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/390857The aim of this paper, firstly, is to construct generating functions of q-Euler numbers and polynomials of higher order by applying the fermionic p-adic q-Volkenborn integral, secondly, to define multivariate q-Euler zeta function (Barnes-type Hurwitz q-Euler zeta function) and l-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz q-Euler zeta function and multivariate q-Euler l-function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well.Hacer Ozden, Ismail Naci Cangul, and Yilmaz Simsek© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/192679Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods.Thomas Bonesky, Kamil S. Kazimierski, Peter Maass, Frank Schöpfer, and Thomas Schuster© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/237937Weighted Lp for p∈(1,∞) and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.Guoen Hu, Haibo Lin, and Dachun Yang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/765920For any n, the contour integral y=coshn+1x∮C(cosh(zs)/(sinhz-sinhx)n+1dz,s2=-λ, is associated with differential equation d2y(x)/dx2+(λ+n(n+1)/cosh2x)y(x)=0. Explicit solutions for n=1 are obtained. For n=1, eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored. This differential equation which does have solution in terms of the trigonometric functions does not seem to have been explored and it is also one of the purposes of this paper to put it on record.Tanfer Tanriverdi and JohnBryce Mcleod© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/295817The attainable sets of the nonlinear control systems with integral constraint on the control functions are considered. It is assumed that the behavior of control system is described by differential equation which is nonlinear with respect to phase-state vector and control vector. The admissible control functions are chosen from the closed ball centered at the origin with radius μ0 in Lp([t0,θ];ℝm) (p∈(1,+∞)). Precompactness of the solutions set is specified, and dependence of the attainable sets on the initial conditions and on the parameters of the control system is studied.Khalik G. Guseinov and Ali S. Nazlipinar© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/381791We consider an integral variational control system on a Banach space X and we study the connections between its uniform exponential stability and the (I(ℝ+,X),O(ℝ+,X)) stability, where I and O are Banach function spaces. We identify the viable classes of input spaces and output spaces related to the exponential stability of systems and provide optimization techniques with respect to the input space. We analyze the robustness of exponential stability in the presence of structured perturbations. We deduce general estimations for the lower bound of the stability radius of a variational control system in terms of input-output operators acting on translation-invariant spaces. We apply the main results at the study of the exponential stability of nonautonomous systems and analyze in the nonautonomous case the robustness of this asymptotic property.Bogdan Sasu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/651294Using some techniques from vector integration, we prove the weak measurability of the adjoint of strongly continuous semigroups which factor through Banach spaces without isomorphic copy of l1; we also prove the strong continuity away from zero of the adjoint if the semigroup factors through Grothendieck spaces. These results are used, in particular, to characterize the space of strong continuity of {T**(t)}t≥0, which, in addition, is also characterized for abstract L- and M-spaces. As a corollary, it is proven that abstract L-spaces with no copy of l1 are finite-dimensional.Diómedes Bárcenas and Luis Gerardo Mármol© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/756934Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function u, and prove that the set of bifurcation points for the solutions of the system is not σ-compact. Then, we deal with a linear system depending on a real parameter λ>0 and on a function u, and prove that there exists λ∗ such that the set of the functions u, such that the system admits nontrivial solutions, contains an accumulation point.Francesca Faraci and Antonio Iannizzotto© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/127394The existence and uniqueness of global mild solutions are proven for a class of semilinear nonautonomous evolution equations. Moreover, it is shown that the system, under considerations, has a unique steady state. This analysis uses, essentially, the dissipativity, a subtangential condition, and the positivity of the related C0-semigroup.B. Aylaj, M. E. Achhab, and M. Laabissi© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/153285We provide new variational settings to study the a.p. (almost periodic) solutions of a class of nonlinear neutral delay equations. We extend Shu and Xu (2006) variational setting for periodic solutions of nonlinear neutral delay equation to the almost periodic settings. We obtain results on the structure of the set of the a.p. solutions, results of existence of a.p. solutions, results of existence of a.p. solutions, and also a density result for the forced equations.M. Ayachi and J. Blot© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/531361For variational inequalities, various merit functions, such as the gap function, the regularized gap function, the D-gap function and so on, have been proposed. These functions lead to equivalent optimization formulations and are used to optimization-based methods for solving variational inequalities. In this paper, we extend the regularized gap function and the D-gap functions for a quasi-variational inequality, which is a generalization of the variational inequality and is used to formulate generalized equilibrium problems. These extensions are shown to formulate equivalent optimization problems for quasi-variational inequalities and are shown to be continuous and directionally differentiable.Kouichi Taji© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/829701We consider the initial value problem for a functional differential inclusion with a Volterra multivalued mapping that is not necessarily decomposable in L1n[a,b]. The concept of the decomposable hull of a set is introduced. Using this concept, we define a generalized solution of such a problem and study its properties. We have proven that standard results on local existence and continuation of a generalized solution remain true. The question on the estimation of a generalized solution with respect to a given absolutely continuous function is studied. The density principle is proven for the generalized solutions. Asymptotic properties of the set of generalized approximate solutions are studied.Anna Machina, Aleksander Bulgakov, and Anna Grigorenko© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/246876The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered.Nak Eun Cho© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/653243This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn=f(xn−2)/g(xn−1), n∈ℕ0, where f,g∈C[(0,∞),(0,∞)]. It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone. For the case when f(x)=α+βx and g satisfies the conditions g(0)=1, g is nondecreasing, and x/g(x) is increasing, we prove that every prime periodic solution of the equation has period equal to one or two. We also investigate the global periodicity of the equation, showing that if all solutions of the equation are periodic with period three, then f(x)=c1/x and g(x)=c2x, for some positive c1 and c2.Stevo Stević and Kenneth S. Berenhaut© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/35151In 2006, W. G. Park and J. H. Bae investigated the Hyers-Ulam stability of a Cauchy-Jensen functional equation. In this paper, we improve their results and obtain better results for a Cauchy-Jensen functional equation. Also, we establish new theorems for the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation.Kil-Woung Jun, Yang-Hi Lee, and Young-Sun Cho© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/37217By using the strong monotonicity of the perturbed fixed-point map and the normal map associated with cocoercive variational inequalities, we establish two new global bounds measuring the distance between any point and the solution set for cocoercive variational inequalities.Fan Jianghua and Wang Xiaoguo© 2008, Hindawi Publishing Corporation. All rights reserved.