http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/363012.htmlA convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its ϵ-approximate solutions, and then we prove ϵ-weak duality theorem and ϵ-strong duality theorem which hold between the problem and its Wolfe type dual problem. Moreover, we give an example illustrating the duality theorems.Gue Myung Lee and Jae Hyoung Lee© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/865096.htmlWe estimate Lyapunov inequalities for a single equation, a cycled system and a coupled system of one-dimensional p-Laplacian problems with weight functions having stronger singularities than L1.Inbo Sim and Yong-Hoon Lee© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/897123.htmlWe will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x+y)±g(x−y)=λf(x)g(y) andf(x+y)±g(x−y)=λg(x)f(y), which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.Gwang Hui Kim© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/931275.htmlIn this paper, we establish a general refinement of the Becker-Stark inequalities by using the power series expansion of the tangent function via Bernoulli numbers and the property of a function involving Riemann's zeta one.Ling Zhu and Jiukun Hua© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/717341.htmlThe purpose of this paper is to introduce an iterative algorithm for finding a solution of quadratic minimization problem in the set of fixed points of a nonexpansive mapping and to prove a strong convergence theorem of the solution for quadratic minimization problem. The result of this article improved and extended the result of G. Marino and H. K. Xu and some others.Li Liu, Guanghui Gu, and Yongfu Su© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/423792.htmlSavas and Mursaleen defined the notions of statistically convergent and statistically Cauchy for double sequences of fuzzy numbers. In this paper, we continue the study of statistical convergence by proving some theorems.Ekrem Savaş and Richard F. Patterson© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/251761.htmlWe introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings and monotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inverse-strongly monotone mappings, which is a solution of a certain variational inequality. Our results substantially develop and improve the corresponding results of [Chen et al. 2007 and Iiduka and Takahashi 2005]. Essentially a new approach for finding the fixed points of nonexpansive mappings and solutions of variational inequalities for monotone mappings is provided.Jong Soo Jung© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/290124.htmlThe definitions and properties of moment of gλ random variable are provided on Sugeno measure space. Then some important moment estimation inequalities based on gλ random variable are presented and proven.Jingfeng Tian, Zhiming Zhang, and Dazeng Tian© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/698012.htmlWe present a new method to study analytic inequalities involving n variables. Regarding its applications, we proved some well-known inequalities and improved Carleman's inequality.Xiao-Ming Zhang and Yu-Ming Chu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/624631.htmlWe shall introduce and construct explicitly the complementary Lidstone interpolating polynomial P2m(t) of degree 2m, which involves interpolating data at the odd-order derivatives. For P2m(t) we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a (2m+1)th order differential equation and the complementary Lidstone boundary conditions.Ravi P. Agarwal, Sandra Pinelas, and Patricia J. Y. Wong© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/503203.htmlWe study some limit properties of the harmonic mean of random transition probability for a second-order nonhomogeneous Markov chain and a nonhomogeneous Markov chain indexed by a tree. As corollary, we obtain the property of the harmonic mean of random transition probability for a nonhomogeneous Markov chain.Zhiyan Shi and Weiguo Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/192197.htmlBy using the way of weight functions and the technic of real analysis, a multiple Hilbert-type integral operator with the homogeneous kernel of −λ-degree (λ∈R) and its norm are considered. As for applications, two equivalent inequalities with the best constant factors, the reverses, and some particular norms are obtained.Qiliang Huang and Bicheng Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/498631.htmlIn the previous paper by the first and the third authors, we present six algorithms for determining whether a given symmetric matrix is strictly copositive, copositive (but not strictly), or not copositive. The algorithms for matrices of order n≥8 are not guaranteed to produce an answer. It also shows that for 1000 symmetric random matrices of order 8, 9, and 10 with unit diagonal and with positive entries all being less than or equal to 1 and negative entries all being greater than or equal to −1, there are 8, 6, and 2 matrices remaing undetermined, respectively. In this paper we give two more algorithms for n=8,9 and our experiment shows that no such matrix of order 8 or 9 remains undetermined; and almost always no such matrix of order 10 remains undetermined. We also do some discussion based on our experimental results.Yang Shang-jun, Xu Chang-qing, and Li Xiao-xin© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/253040.htmlUsing the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation: f(x+2y)+f(x−2y)=2f(x+y)+2f(−x−y)+2f(x−y)+2f(y−x)−4f(−x)−2f(x)+f(2y)+f(−2y)−4f(y)−4f(−y) in fuzzy Banach spaces.Choonkil Park© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/437976.htmlWe use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE) in Hilbert spaces. The algorithm for finding a solution of the problem (SMIE) is suggested; the convergence criteria and stability of the iterative algorithm are discussed. The results presented in this paper are more general and are viewed as an extension, refinement, and improvement of the previously known results in the literature.Yeol Je Cho and Narin Petrot© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/645498.htmlWe consider viscosity approximation methods with demi-continuous strong pseudo-contractions for a non-expansive semigroup. Strong convergence theorems of the purposed iterative process are established in the framework of Hilbert spaces.Changqun Wu, Sun Young Cho, and Meijuan Shang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/869684.htmlThe purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.Shih-sen Chang, Jong Kyu Kim, and Xiong Rui Wang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/801961.htmlThe purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001), Cho et al. (2005), Ofoedu (2006), Schu (1991) and Zeng (2003 and 2005), and many others.Feng Gu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/847357.htmlSome new upper and lower bounds on determinants are presented for diagonally dominant matrices and general H-matrices by using different methods. These bounds are some improvements of results given by Ostrowski (1952) and (1937), Price (1951), Wang and Zhang (2002), Huang and Liu (2005), and so forth. In addition, these bounds are also used to localize some numerical characters (e.g., the minimum eigenvalues, singular values and condition numbers) of certain matrices.Hou-Biao Li, Ting-Zhu Huang, and Hong Li© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/597569.htmlWe consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic solutions, that is, all non-trivial nonnegative solutions of the initial boundary value problem, will lie between a minimal and a maximal nonnegative nontrivial periodic solutions, as time tends to infinity.Jiebao Sun, Boying Wu, and Dazhi Zhang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/410576.htmlUsing the fixed point method, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional inequality and of the Cauchy-Jensen additive functional inequality in fuzzy Banach spaces.Choonkil Park© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/182576.htmlWe propose a new projection algorithm for generalized variational inequality with multivalued mapping. Our method is proven to be globally convergent to a solution of the variational inequality problem, provided that the multivalued mapping is continuous and pseudomonotone with nonempty compact convex values. Preliminary computational experience is also reported.Changjie Fang and Yiran He© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/763252.htmlFor p∈ℝ, the generalized logarithmic mean Lp of two positive numbers a and b is defined as Lp(a,b)=a, for a=b, LP(a,b)=[(bp+1−ap+1)/(p+1)(b−a)]1/p , for a≠b, p≠−1, p≠0, LP(a,b)=(b−a)/(log⁡b−log⁡a), for a≠b, p=−1, and LP(a,b)=(1/e)(bb/aa)1/(b−a) , for a≠b, p=0. In this paper, we prove that G(a,b)+H(a,b)⩾2L−7/2(a,b),A(a,b)+H(a,b)⩾2L−2(a,b), and L−5(a,b)⩾H(a,b) for all a,b>0, and the constants −7/2,−2, and −5 cannot be improved for the corresponding inequalities. Here A(a,b)=(a+b)/2=L1(a,b),G(a,b)=ab=L−2(a,b), and H(a,b)=2ab/(a+b) denote the arithmetic, geometric, and harmonic means of a and b, respectively.Yu-Ming Chu and Wei-Feng Xia© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/486325.htmlWe obtain the superstability of the Pexiderized multiplicative functional equation f(xy)=g(x)h(y) and investigate the stability of this equation in the following form: 1/(1+ψ(x,y))≤f(xy)/g(x)h(y)≤1+ψ(x,y).Young Whan Lee© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2010/968271.htmlWe introduce and study a class of η-generalized vector variational-like inequalities and a class of η-generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces. An equivalence result concerned with two classes of η-generalized vector variational-like inequalities is proved under suitable conditions. By using FKKM theorem, some new existence results of solutions for the η-generalized vector variational-like inequalities and η-generalized strong vector variational-like inequalities are obtained under some suitable conditions.Xi Li, Jong Kyu Kim, and Nan-Jing Huang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/503948.htmlWe consider generalized Morrey spaces ℳp,ω(ℝn) with a general function ω(x,r) defining the Morrey-type norm. We find the conditions on the pair (ω1,ω2) which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space ℳp,ω1(ℝn) to another ℳp,ω2(ℝn), 1<p<∞, and from the space ℳ1,ω1(ℝn) to the weak space Wℳ1,ω2(ℝn). We also prove a Sobolev-Adams type ℳp,ω1(ℝn)→ℳq,ω2(ℝn)-theorem for the potential operators Iα. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities on (ω1,ω2), which do not assume any assumption on monotonicity of ω1,ω2 in r. As applications, we establish the boundedness of some Schrödinger type operators on generalized Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class. As an another application, we prove the boundedness of various operators on generalized Morrey spaces which are estimated by Riesz potentials.Vagif S. Guliyev© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/153080.htmlWe give the best possible global bounds for a form of discrete Jensen's inequality. By some examples the fruitfulness of this result is shown.Slavko Simic© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/515709.htmlLet p(z) be a polynomial of degree n and for any real or complex number α, and let Dαp(z)=np(z)+(α−z)p′(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain new results concerning the maximum modulus of a polar derivative of a polynomial with restricted zeros. Our results generalize as well as improve upon some well-known polynomial inequalities.M. Bidkham, M. Shakeri, and M. Eshaghi Gordji© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/127431.htmlWe study the boundedness and compactness of differences of weighted composition operators on weighted Banach spaces in the unit ball of CN.Jineng Dai and Caiheng Ouyang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/491576.htmlWe prove an interesting extension of the Shapiro's cyclic inequality for four and five variables and formulate a generalization of the well-known Shapiro's cyclic inequality. The method used in the proofs of the theorems in the paper concerns the positive quadratic forms.Nguyen Minh Tuan and Le Quy Thuong© 2010, Hindawi Publishing Corporation. All rights reserved.