A new type of fixed point theorem in metric spaces

We prove a generalization of Edelstein’s fixed point theorem. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem.     

浊点萃取-流动注射电感耦合等离子体原子发射光谱法同时测定水中镉钴铜镍锌

本文提出了浊点萃取-流动注射电感耦合等离子体原子发射光谱（FI—ICP—AES）法同时测定水中镉、钴、铜、镍、锌的新方法。利用5-Br—PADAP将待测金属离子转化为水不溶性的螯合物，并萃取到表面活性剂Triton X-114的浓缩相，以乙醇-硝酸溶液稀释含富集离子的浓缩相，并以FI—ICP-AES法测定。考察了流动注射进样体积、积分时间、萃取体系介质酸度、螯合剂和表面活性剂用量等实验条件的影响。在折衷条件下，镉、钴、铜、镍和锌的浓缩倍率可达18、10、16、10和8，检出限分别为0．7μg／L、1．6μg／L、1．3μg／L、5．7μg／L、3．2μg／L。方法成功应用于自来水、河水和海水中痕量镉、钴、铜、镍和锌的分析。在0．02mg／L和0．10mg／L二个水平进行加入回收试验，回收率在80％与118％之间。     

Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application

In this paper, fixed point theorems of Rothe and Altman types about convex-power condensing operator are given and applied to the differential equation of one order with integral boundary conditions in abstract space.     

Criteria for farthest points on convex surfaces

We provide a sharp, sufficient condition to decide if a point y on a convex surface S is a farthest point (i.e., is at maximal intrinsic distance from some point) on S, involving a lower bound π on the total curvature ω_y at y, ω_y ≥ π. Further consequences are obtained when ω_y > π, and sufficient conditions are derived to guarantee that a convex cap contains at least one farthest point. A connection between simple closed quasigeodesics O of S, points y ∈ S\O with ω_y > π, and the set ?? of all farthest points on S, is also investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.     

Error bounds for approximations of traces of products of truncated Toeplitz operators

The paper establishes error orders for integral limit approximations to the traces of products of truncated Toeplitz operators generated by integrable real symmetric functions defined on the real line. These approximations and the corresponding error bounds are of importance in the statistical analysis of continuous-time stationary processes (asymptotic distributions and large deviations of Toeplitz type quadratic functionals, estimation of the spectrum, etc.). The results improve the rates obtained by the authors (in an earlier paper). An explicit second-order asymptotic expansion is found for the trace of a product of two truncated Toeplitz operators generated by the spectral densities of continuous-time stationary fractional Riesz-Bessel motions. The order of magnitude of the second term in this expansion is shown to depend on the long-memory parameters of the processes. The second-order term provides a substantially better approximation to the original functional, as compared with the first-order approximation. M. Ginovyan research was partially supported by National Science Foundation Grant #DMS-0706786.     

On the stability of the additive Cauchy functional equation in random normed spaces

Some stability results for the functional equations of Cauchy and Jensen in probabilistic setting are proved by using the fixed point method.     

Fixed point theorems for generalized contractions in ordered metric spaces

The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petru?el, I.A. Rus [A. Petru?el, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.     

Block monotone iterative algorithms for variational inequalities with nonlinear operators

Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.     

On the Analysis of the Virtual Waiting Time in Open Queueing Networks

The model of an open queueing network in heavy traffic has been developed. These models are mathematical models of computer networks in heavy traffic. A limit theorem has been presented for the virtual waiting time of a customer in heavy traffic in open queueing networks. Finally, we present an application of the theorem—a reliability model from computer network practice.