http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/369185.htmlThe exponential stability of singularly perturbed impulsive delay integrodifferential equations (SPIDIDEs) is concerned. By establishing an impulsive delay integrodifferential inequality (IDIDI), some sufficient conditions ensuring the exponentially stable of any solution of SPIDIDEs for sufficiently small ε>0 are obtained. A numerical example shows the effectiveness of our theoretical results.Danhua He and Liguang Xu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/732106.htmlThe axi-symmetric Young-Laplace differential equation is analyzed. Solutions of this equation can describe the outer or inner free surface of a static meniscus (the static liquid bridge free surface between the shaper and the crystal surface) occurring in single crystal tube growth. The analysis concerns the dependence of solutions of the equation on a parameter p which represents the controllable part of the pressure difference across the free surface. Inequalities are established for p which are necessary or sufficient conditions for the existence of solutions which represent a stable and convex outer or inner free surfaces of a static meniscus. The analysis is numerically illustrated for the static menisci occurring in silicon tube growth by edge-defined film-fed growth (EFGs) technique. This kind of inequalities permits the adequate choice of the process parameter p. With this aim this study was undertaken.Stefan Balint and Agneta M. Balint© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/458134.htmlThe efficiency of the implicit method proposed by He (1999) depends on the parameter β heavily; while it varies for individual problem, that is, different problem has different “suitable” parameter, which is difficult to find. In this paper, we present a modified implicit method, which adjusts the parameter β automatically per iteration, based on the message from former iterates. To improve the performance of the algorithm, an inexact version is proposed, where the subproblem is just solved approximately. Under mild conditions as those for variational inequalities, we prove the global convergence of both exact and inexact versions of the new method. We also present several preliminary numerical results, which demonstrate that the self-adaptive implicit method, especially the inexact version, is efficient and robust.Zhili Ge and Deren Han© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/730132.htmlWe show strong and Δ convergence for Mann iteration of a multivalued nonexpansive mapping whose domain is a nonempty closed convex subset of a CAT(0) space. The results we obtain are analogs of Banach space results by Song and Wang [2009, 2008]. Strong convergence of Ishikawa iteration are also included.W. Laowang and B. Panyanak© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/147069.htmlThe purpose of the present paper is to investigate some inclusion properties of certain classes of meromorphic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some invariant properties under convolution are also considered for the classes presented here. The results presented here include several previous known results as their special cases.Nak Eun Cho© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/865093.htmlWe introduce and study a new class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces. By using the Chang's lemma and the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang (2001), we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative procedures with errors for this nonlinear random multivalued operator equations in q-uniformly smooth Banach spaces. The results presented in this paper improve and generalize some known corresponding results in iterature.Heng-You Lan, Yeol Je Cho, and Wei Xie© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/813687.htmlWe establish a relation between the functions of bounded boundary and bounded radius rotations by using three different techniques. A well-known result is observed as a special case from our main result. An interesting application of our work is also being investigated.K. I. Noor, W. Ul-Haq, M. Arif, and S. Mustafa© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/807943.htmlThe main object of the present paper is to investigate univalence and starlikeness of certain integral operators, which are defined here by means of hypergeometric functions. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.R. Aghalary and A. Ebadian© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/494257.htmlA Hilbert-type linear operator T:ℓϕp→ℓψp is defined. As for applications, a more precise operator inequality with the norm and its equivalent forms are deduced. Moreover, three equivalent reverses from them are given as well. The constant factors in these inequalities are proved to be the best possible.Wuyi Zhong© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/290713.htmlWe introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber's inequalities, Nalder's results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximation-solvability of the nonlinear operator equations in Banach spaces. The results presented in this paper improve and generalize the corresponding results on strongly monotone quasivariational inclusions and nonlinear implicit quasivariational inclusions.Xing Wei, Heng-you Lan, and Xian-jun Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/357349.htmlThe purpose of this paper is to find Hölder type inequality for the fermionic p-adic invariant q-integral which was defined by Kim (2008).Lee-Chae Jang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/852406.htmlThe spectral radius ρ(G) of a graph G is the largest eigenvalue of its adjacency matrix. Let λ(G) be the smallest eigenvalue of G. In this paper, we have described the K3,3-minor free graphs and showed that (A) let G be a simple graph with order n≥7. If G has no K3,3-minor, then ρ(G)≤1+3n−8. (B) Let G be a simple connected graph with order n≥3. If G has no K3,3-minor, then λ(G)≥−2n−4, where equality holds if and only if G is isomorphic to K2,n−2.Kun-Fu Fang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/819036.htmlWe establish strong convergence theorem for multi-step iterative scheme with errors for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces. Our results extend and improve the recent ones announced by Plubtieng and Wangkeeree (2006), and many others.Feng Gu and Qiuping Fu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/489061.htmlWe study the mixed initial-boundary value problem for hyperbolic system of second order outside a closed domain. The existence of solutions to this problem is proved and the estimate for the regularity of solutions is given. The application of the existence theorem to elastrodynamics is discussed.Jie Xin and Xiuyan Sha© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/864191.htmlThe Meda inequality for rearrangements of the convolution operator on the Heisenberg group ℍn is proved. By using the Meda inequality, an O'Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator MΩ,α and fractional integral operator IΩ,α with rough kernels in the spaces Lp(ℍn) are found. Finally, we give some comments on the extension of our results to the case of homogeneous groups.V. S. Guliyev, A. Serbetci, E. Güner, and S. Balcı© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/934321.htmlWe introduce a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus of Banach space X. Some basic properties of this new coefficient are investigated. Moreover, some sufficient conditions which imply normal structure are presented.Zhanfei Zuo and Yunan Cui© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/214530.htmlRecently, Baktash et al. (2008) proved the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) and the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. In this note, we correct the proofs.R. Saadati, S. M. Vaezpour, and Y. J. Cho© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/170526.htmlWe use inequality technique and the terminating case of the q-binomial formula to give some results on convergence of q-series involving ϕr+1r basic hypergeometric series. As an application of the results, we discuss the convergence for special Thomae q-integral.Mingjin Wang and Xilai Zhao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/649427.htmlAn exponential inequality is established for identically distributed negatively associated random variables which have the finite Laplace transforms. The inequality improves the results of Kim and Kim (2007), Nooghabi and Azarnoosh (2009), and Xing et al. (2009). We also obtain the convergence rate O(1)n1/2(log⁡n)−1/2 for the strong law of large numbers, which improves the corresponding ones of Kim and Kim, Nooghabi and Azarnoosh, and Xing et al.Soo Hak Sung© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/702680.htmlWe obtain an estimate on the rate of convergence of Durrmeyer-Bézier operaters for functions of bounded variation by means of some probabilistic methods and inequality techniques. Our estimate improves the result of Zeng and Chen (2000).Pinghua Wang and Yali Zhou© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/620758.htmlBy using singular value decomposition and majorization inequalities, we propose new inequalities for the trace of the product of two arbitrary real square matrices. These bounds improve and extend the recent results. Further, we give their application in the algebraic Riccati equation. Finally, numerical examples have illustrated that our results are effective and superior.Jianzhou Liu and Juan Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/393940.htmlNew concepts of generalized (ρ,θ)-η invex functions for non-differentiable functions and generalized (ρ,θ)-η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized (ρ,θ)-η invexity of functions and generalized (ρ,θ)-η invariant monotonicity of the corresponding Clarke's subdifferentials are studied. Some of our results are extension and improvement of some results obtained in (Jabarootion and Zafarani (2006); Behera et al. (2008)).Caiping Liu and Xinmin Yang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/193169.htmlA generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order k (k≥2) for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.Ahmed Alsaedi and Bashir Ahmad© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/461757.htmlA new singular impulsive delay differential inequality is established. Using this inequality, the invariant and attracting sets for impulsive neutral neural networks with delays are obtained. Our results can extend and improve earlier publications.Zhixia Ma and Xiaohu Wang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/628051.htmlWe discuss log-convexity for the differences of the Popoviciu inequalities and introduce some mean value theorems and related results. Also we give the Cauchy means of the Popoviciu type and we show that these means are monotonic.Matloob Anwar, Naveed Latif, and J. Pečarić© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/390634.htmlThe existence of common fixed points is established for the mappings, where T is (f,θ,L)-weak contraction on a nonempty subset of a Banach space. As application, some results on the invariant best approximation are proved. Our results unify and substantially improve several recent results given by some authors.Nawab Hussain and Yeol Je Cho© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/676373.htmlWe present some sufficient conditions for which a Banach space X has normal structure in terms of the modulus of U-convexity, modulus of W∗-convexity, and the coefficient R(1,X), which generalized some well-known results. Furthermore the relationship between modulus of convexity, modulus of smoothness, and Gao's constant is considered, meanwhile the exact value of Milman modulus has been obtained for some Banach space.Zhanfei Zuo and Yunan Cui© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/710475.htmlWe first prove a generalized Wirtinger's inequality. Then, applying the inequality, we study estimates for lower bounds of periods of periodic solutions for a class of delay differential equations x˙(t)=−∑k=1nf(x(t−kr)), and x˙(t)=−∑k=1ng(t,x(t−ks)), where x∈ℝp, f∈C(ℝp,ℝp), and g∈C(ℝ×ℝp,ℝp) and r>0, s>0 are two given constants. Under some suitable conditions on f and g, lower bounds of periods of periodic solutions for the equations aforementioned are obtained.Rong Cheng and Dongfeng Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/258569.htmlWe establish some new nonlinear Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of differential equations. Example of applying these inequalities to derive the properties of BVPs is also given.Chur-Jen Chen, Wing-Sum Cheung, and Dandan Zhao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/jia/2009/946569.htmlThe aim of this paper is to construct p-adic twisted two-variable Euler-(h,q)-L-functions, which interpolate generalized twisted (h,q)-Euler polynomials at negative integers. In this paper, we treat twisted (h,q)-Euler numbers and polynomials associated with p-adic invariant integral on ℤp. We will construct two-variable twisted (h,q)-Euler-zeta function and two-variable (h,q)-L-function in Complex s-plane.Kyoung Ho Park© 2009, Hindawi Publishing Corporation. All rights reserved.