Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings

In this paper we propose and analyze three parallel hybrid extragradient methods for finding a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of fixed points of nonexpansive mappings in a real Hilbert space. Based on parallel computation we can reduce the overall computational effort under widely used conditions on the bifunctions and the nonexpansive mappings. A simple numerical example is given to illustrate the proposed parallel algorithms.     

异步并行非线性对称Gauss-Seidel迭代算法

1．引言考虑非线性方程组其中A＝（a。。）EL（＊”）为＊一矩阵，B＝（衬。）EL（＊”）为非负矩阵，呐X）一（p。（X。》，4（二）＝（吵k（kk》：＊一＊一为连续的对角映射，而6＝（6k）E＊一为已知向量．这里，什小：”一”均可微，但二者的导函数并不一定连续．这类方程组具有丰富的实际背景．例如，描述冰体溶解过程的著名的Stefan问题，就可归结为问题（1·1）的数值求解（见［l］）．为在多处理机系统上有效地求解问题（1．1），文山利用这类非线性方程组的特殊结构，建立了一类并行非线性Gauss—Seidel型迭代算法．为避免该算…     

Iterative Methods for Nonexpansive Mappings in Banach Spaces

In this article, we suggest and analyze two methods for finding fixed points of nonexpansive mappings in Banach spaces. We prove that the proposed methods converge strongly to a fixed point of nonexpansive mappings.     

A strong convergence theorem for solving the split feasibility and fixed point problems in Banach spaces

In this paper, we introduce a new parallel iterative method for finding a common solution of the multiple-set split feasibility and fixed point problems concerning left Bregman strongly nonexpansive mappings in Banach spaces.     

Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces

In this paper, building upon projection methods and parallel splitting-up techniques with using proximal operators, we propose new algorithms for solving the multivalued lexicographic variational inequalities in a real Hilbert space. First, the strong convergence theorem is shown with Lipschitz continuity of the cost mapping, but it must satisfy a strongly monotone condition. Second, the convergent results are also established to the multivalued lexicographic variational inequalities involving a finite system of demicontractive mappings under mild assumptions imposed on parameters. Finally, some numerical examples are developed to illustrate the behavior of our algorithms with respect to existing algorithms.     

实Hilbert空间中一个拟非扩张映射有限族的公共不动点的粘滞逼近算法

本文构造了两种平行算法, 用来解决实Hilbert空间中有限多个拟非扩张映射的公共不动点的问题,这两种算法改进完善了本方向以前所得的结果.     

集值映射空间上的基数函数

讨论了集值映射空间在赋予点态收敛拓扑或紧开拓扑下的权数,特征,网络权,稠密度等基数函数,利用自然映射,诱导映射和嵌入等方法将单值连续映射空间的有关结论推广到集值映射空间类上.     

两类拟共形映射的掩盖定理

In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.     

Algorithmes parallèles asynchrones pour des systèmes singuliers

In this paper we give a convergence result concerning parallel bounded delayed asynchronous algorithms for linear fixed point problems with nonexpansive linear mappings with respect to a weighted maximum norm. This allows us to propose parallel algorithms which converge to the solution of consistent singular systems, including singular M-matrices (see for more details [3]). An important characteristic of our technical framework is that we are able to describe two-stage algorithms.     

Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces

In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Chen et al. [J.M. Chen, L.J. Zhang, T.G. Fan, Viscosity approximation methods for nonexpansive mappings and monotone mappings, doi:10.1016/j.jmaa.2006.12.088], Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350], Yao and Yao [Y.H. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput, doi:10.1016/j.amc.2006.08.062] and Many others.     

Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings

In this paper, we introduce some implicit iterative algorithms for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. These implicit iterative algorithms are based on two well-known methods: extragradient and approximate proximal methods. We obtain some weak convergence theorems for these implicit iterative algorithms. Based on these theorems, we also construct some implicit iterative processes for finding a common fixed point of two mappings, such that one of these two mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the other mapping is asymptotically nonexpansive.     

局部单叶对数调和映射的Bohr半径

本文研究了一类局部单叶对数调和映射的若干性质.利用复分析的方法与技巧,获得了该类映射的增长定理和两种新的Bohr半径,推广了几何函数的理论研究结果.     

有限偏差函数与调和函数

分别借助解析函数与调和函数两类函数的Dirichlet积分,利用相关文献给定边界值的拟共形映射极值伸缩商的估计方法,通过有限偏差函数和拟共形映射的关系估计了具有给定边界值的有限偏差函数的极值伸缩商.得到了解析函数的Dirichlet积分在有限偏差函数下具有拟不变性,同时给出有限偏差函数极值伸缩商的下界估计.     

ISomorphismen verallgemeinerter Parallelstrukturen

Incidencestructures with an equivalence relation on the set of blocks or lines, satisfying the euclidean axiom of parallelism, are called generalised parallel structures, if on each line are at least two points and if through two different points passes at most one line. In this paper we give a coordinatization for a class of generalised parallel structures. Isomorphisms of desarguesian affine spaces induce in a well known manner regular semilinear mappings of the corresponding vector spaces. We prove an analogous theorem for generalised parallel structures and the corresponding algebraic structures.     

The common minimal-norm fixed point of a finite family of nonexpansive mappings

Consider a finite family of nonexpansive mappings which are defined on a closed convex subset of a Hilbert space H. Suppose the set of common fixed points of this family is nonempty. We then address the problem of finding the minimum-norm element of this common fixed point set. We introduce both cyclic and parallel iteration methods to find this minimal-norm element.     

Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces

In this paper, we prove a strong convergence theorem of Halpern’s type for 2-generalized hybrid mappings in a Hilbert space. We also deal with strong convergence theorems by hybrid methods for these nonlinear mappings in a Hilbert space.     

An operator splitting method for monotone variational inequalities with a new perturbation strategy

In variational inequalities arising from applications such as engineering, economics and transportation, partial mappings are usually unknown, e.g., the demand function in traffic assignment problem. As a consequence, classical methods can not deal with this class of problems. On the other hand, the recently developed methods require restrictive conditions such as strong monotonicity of some mappings, which excludes many interesting applications. In this paper, we propose an operator splitting method with a new perturbation strategy for solving variational inequality problems with partially unknown mappings. Under the mild condition that the underlying mapping is monotone, we prove the global convergence of the method. We also report some preliminary numerical results which show that the new algorithm is also interesting from the numerical point of view.     

Novel Hybrid Methods for Pseudomonotone Equilibrium Problems and Common Fixed Point Problems

The purpose of this article is to introduce some hybrid algorithms for finding a common element of the solution sets of pseudomonotone equilibrium problems and the fixed point sets of nonexpansive mappings in real Hilbert spaces. Our algorithms combine Mann’s iterative methods and Armijo line-search with parallel splitting-up and hybrid techniques. The strong convergence of the proposed algorithms are established without the assumption on the Lipschitz-type condition for the bifunctions involved.     

A New Class of Monotone Mappings and a New Class of Variational Inclusions in Banach Spaces

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associated with this mappings and show its Lipschitz continuity. By using the technique of proximal mapping, we construct a new iterative algorithm. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known results.     

Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces

We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods of proof mining to obtain an explicit quantitative version of a generalization to geodesic spaces of a result on the asymptotic behavior of Picard iterates for firmly nonexpansive mappings proved by Reich and Shafrir. From this result we obtain effective uniform bounds on the asymptotic regularity for firmly nonexpansive mappings. Besides this, we derive effective rates of asymptotic regularity for sequences generated by two algorithms used in the study of the convex feasibility problem in a nonlinear setting.