向量拟平衡问题系统及其应用

引入了向量拟平衡问题系统并证明了其解的存在性定理．作为应用,还得到约束多目标对策和无约束多目标对策弱Pareto平衡的一些存在性结果．     

集值映射的广义对称向量拟平衡问题系统

In this paper, a system of generalized symmetric vector quasi-equilibrium problems for set-valued mappings is introduced. By using a scalarization method and a fixed-point theorem, the existence result for its solution is established. The main result extends the corresponding results in Fu （J. Math. Anal. Appl. 285, 708-713, 2003） and Zhang, Chen and Li （OR Transactions 10, 24-32, 2006）.     

On System of Generalized Vector Quasi-equilibrium Problems with Set-valued Maps

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.     

局部FC-一致空间内具有联立广义矢量拟平衡组约束的数学规划(英文)

在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理.     

System of Vector Equilibrium Problems and Its Applications

In this paper, we introduce a system of vector equilibrium problems andprove the existence of a solution. As an application, we derive someexistence results for the system of vector variational inequalities. We alsoestablish some existence results for the system of vector optimizationproblems, which includes the Nash equilibrium problem as a special case.     

Generalized Variation of Mappings with Applications to Composition Operators and Multifunctions

We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV (I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV (I;X) GV (I;Y) is Lipschitzian if and only if h(t,x)=h₀(t)+h₁(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.     

On Nondifferentiable and Nonconvex Vector Optimization Problems

In this paper, we prove the equivalence among the Minty vector variational-like inequality, Stampacchia vector variational-like inequality, and a nondifferentiable and nonconvex vector optimization problem. By using a fixed-point theorem, we establish also an existence theorem for generalized weakly efficient solutions to the vector optimization problem for nondifferentiable and nonconvex functions.     

On the Representation of Approximate Subdifferentials for a Class of Generalized Convex Functions

Given a family of real-valued functions defined in a normed vector space X, we study a class of -convex functions having a simpler representation for the --subdifferential. The case =X^* with X being a Banach space (the Fenchel case) is particularly analysed, and we find that the sublinear lower semicontinuous functions satisfy the simpler representation with respect to X^*. As a side result, we provide various new subdifferential-type charaterizations of positively homogeneous functions among those which are lower semicontinuous and convex. In addition, we also discuss that family related to the the so-called prox-bounded functions. In this more general framework our simpler representation may give rise to a new notion of enlargement of the subdifferential.Mathematics Subject Classifications (2000) 47H05, 46B99, 47H17.This work is based on research material supported in part by CONICYT-Chile through FONDECYT 101-0116 and FONDAP-Matemáticas Aplicadas II.     

Strong Approximation for Long Memory Processes with Applications

In this paper we inverstigate the strong approximation of a linear process with long memory to a Gaussian process. The results are then applied to derive the law of the iterated logarithm and Darling–Erds type theorem for long memory processes under ideal conditions.     

The Canonical Decompositions of Some Family of Compact Orientable Hyperbolic 3-Manifolds with Totally Geodesic Boundary

L. Paoluzzi and B. Zimmermann constructed a family of compact orientable hyperbolic 3-manifolds with totally geodesic boundary, and classified them up to homeomorphism. Our main purpose is to determine the canonical decompositions of these manifolds. Using the result, we can obtain an alternative proof of the classification theorem of these manifolds and determine their isometry groups. We also determine their unknotting tunnels. Some of these manifolds are related to certain spatial graphs, so-called Suzukis Brunnian graphs. The properties of these manifolds enable us to obtain those of the graphs. Moreover, we give an affirmative answer to Kinoshitas problem concerning these graphs. In the Appendix, we calculate the volume of these manifolds.     

Harmonic and Refined Extraction Methods for the Singular Value Problem,with Applications in Least Squares Problems

For the accurate approximation of the minimal singular triple (singular value and left and right singular vector) of a large sparse matrix, we may use two separate search spaces, one for the left, and one for the right singular vector. In Lanczos bidiagonalization, for example, such search spaces are constructed. In SIAM J. Sci. Comput., 23(2) (2002), pp. 606–628, the author proposes a Jacobi–Davidson type method for the singular value problem, where solutions to certain correction equations are used to expand the search spaces. As noted in the mentioned paper, the standard Galerkin subspace extraction works well for the computation of large singular triples, but may lead to unsatisfactory approximations to small and interior triples. To overcome this problem for the smallest triples, we propose three harmonic and a refined approach. All methods are derived in a number of different ways. Some of these methods can also be applied when we are interested in the largest or interior singular triples. Theoretical results as well as numerical experiments indicate that the results of the alternative extraction processes are often better than the standard approach. We show that when Lanczos bidiagonalization is used for the subspace expansion, the standard, harmonic, and refined extraction methods are all essentially equivalent. This gives more insight in the success of Lanczos bidiagonalization to find the smallest singular triples. Finally, we show that the extraction processes for the smallest singular values may give an approximation to a least squares problem at low additional costs. The truncated SVD is also discussed in this context. AMS subject classification (2000) 65F15, 65F50, (65F35, 93E24).Submitted December 2002. Accepted October 2004. Communicated by Haesun Park.M. E. Hochstenbach: The research of this author was supported in part by NSF grant DMS-0405387. Part of this work was done when the author was at Utrecht University.     

Relationship between solid cones and cones with bases

This paper establishes a relation between -based cones and solid cones in a separated locally convex topological vector space. The relation reveals that the properties of the base of a based cone affect deeply the topological properties of the dual cone.The author would like to thank Professor C. C. Huang for his discussion on the proof of Corollary 2.1. The author is also grateful to the referees for helpful comments and suggestions.     

The Study of the System of Generalized Vector Quasi-equilibrium Problems

In this paper, we study the system of generalized vector quasi-equilibrium problems, which includes as special cases the system of vector quasi-equilibrium problems and the system of generalized vector equilibrium problems, and establish the existence and essential components of the solution set under perturbations of its best-reply map. Moreover, we also derive a new existence theorem of Ky Fan’s points for a set-valued map.     

Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-Dimensional Lebesgue Measure

We consider some subsets of the Euclidean plane R ², having small linear sections (in all directions), and investigate those sets from the point of view of measurability with respect to certain invariant extensions of the classical Lebesgue measure on R ².     

Non-commutative extrapolation algorithms

This paper contains two general results. The first is an extension of the theory of general linear extrapolation methods to a non-commutative field (or even a non-commutative unitary ring). The second one, by exploiting these new results, is to solve an old conjecture about Wynn's vector -algorithm. Then, by using designants and Clifford algebras, we show how the vectors _k ⁽ⁿ⁾ can be written as a ratio of two designants.This result allow us to find, as a particular case, some well-known results and some others which are new.     

On the Neighbourhood of a Subclass of Univalent Functions Related to Complex Order

We consider the class of functions R(A, B) introduced by Dixit and Pal, where b 0 is a complex number and A, B are fixed members –1 B < A 1. We will study the -neighbourhoods for functions belonging to R^b(A, B), by using convolution techniques.AMS Mathematics Classification (2000): 30C55     

Limit Theorems for Logarithmic Averages of Fractional Brownian Motions

We prove almost sure invariance principles for logarithmic averages of fractional Brownian motions.Research supported byResearch supported by     

Properties of the Set of Extreme Solutions for a Class of Nonlinear Second-Order Evolution Inclusions

We establish the existence of extreme solutions for a class of nonlinear second-order evolution inclusions with a nonconvex right-hand side defined on an evolution triple of Banach spaces. Then we show that extreme solutions which belong to the solution set of the original system are in fact dense and codense in the solution set of a system with a convexified right-hand side. The necessary and sufficient conditions for closedness of the solution set for the original system in an appropriate spaces of functions are given as well. Finally, an example of a nonlinear hyperbolic distributed parameter system is worked out in detail.     

An Illustration of the Power of Structure Theory

There is a hierarchy of concepts of compact semigroups according to the degree of continuity of their multiplications: One-sided continuity, separate continuity, continuity. Each level of generality has its own fields of application and its own peculiarities. This is illustrated in a discussion of three seemingly rather unrelated examples from different branches of mathematics: number theory, functional analysis, logic.