Finding solutions of implicit complementarity problems by isotonicity of the metric projection

Isac and Németh [G. Isac and A. B. Németh, Projection method, isotone projection cones and the complementarity problem, J. Math. Anal. App., 153, 258-275(1990)] proved that solving a coincidence point equation (fixed point problem) in turn solves the corresponding implicit complementarity problem (nonlinear complementarity problem) and they exploited the isotonicity of the metric projection onto isotone projection cones to solve implicit complementarity problems (nonlinear complementarity problems) defined by these cones. In this paper, the notion of *-isotone projection cones is employed and an iterative algorithm is presented in connection with an implicit complementarity problem on *-isotone projection cones. It is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementarity problem. Sufficient conditions are given for this sequence to be convergent for implicit complementarity problems defined by *-isotone projection cones. The question of finding nonzero solutions of these problems is also studied.     

Problems related to a de Bruijn-Erdös theorem

De Bruijn and Erdös proved that every noncollinear set of n points in the plane determines at least n distinct lines. We suggest a possible generalization of this theorem in the framework of metric spaces and provide partial results on related extremal combinatorial problems.     

An iterative approximation method for solving a general system of variational inequality problems and mixed equilibrium problems

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general system of variational inequalities for a cocoercive mapping in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets. Our results extend and improve the corresponding results of Ceng, Wang, and Yao [L.C. Ceng, C.Y. Wang, J.C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Methods Oper. Res. 67 (2008) 375–390], Ceng and Yao [L.C. Ceng, J.C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math. doi:10.1016/j.cam.2007.02.022], Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515] and many others.     

A rate of convergence for asymptotic contractions

In [P. Gerhardy, A quantitative version of Kirk's fixed point theorem for asymptotic contractions, J. Math. Anal. Appl. 316 (2006) 339-345], P. Gerhardy gives a quantitative version of Kirk's fixed point theorem for asymptotic contractions. This involves modifying the definition of an asymptotic contraction, subsuming the old definition under the new one, and giving a bound, expressed in the relevant moduli and a bound on the Picard iteration sequence, on how far one must go in the iteration sequence to at least once get close to the fixed point. However, since the convergence to the fixed point needs not be monotone, this theorem does not provide a full rate of convergence. We here give an explicit rate of convergence for the iteration sequence, expressed in the relevant moduli and a bound on the sequence. We furthermore give a characterization of asymptotic contractions on bounded, complete metric spaces, showing that they are exactly the mappings for which every Picard iteration sequence converges to the same point with a rate of convergence which is uniform in the starting point.     

Hybrid Mann-Halpern iteration methods for nonexpansive mappings and semigroups

In this paper, we introduce some new iteration methods based on the hybrid method in mathematical programming, the Mann’s iterative method and the Halpern’s method for finding a fixed point of a nonexpansive mapping and a common fixed point of a nonexpansive semigroup Hilbert spaces.     

Common Fixed Point Theorems for Finite Number of Mappings without Continuity and Compatibility on Fuzzy Metric Spaces

The aim of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete fuzzy metric spaces. We improve extend and generalize several fixed point theorems on metric spaces,uniform spaces and fuzzy metric spaces.We also give formulas for total number of commutativity conditions for finite number of mappings.     

Metric subregularity and the proximal point method

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for local linear convergence to a zero of a maximal monotone operator. This result is then generalized to obtain convergence rates for the problem of finding a common zero of multiple monotone operators by considering randomized and averaged proximal methods.     

Fuzzy度量空间型映象的不动点定理

本文给出Ｆｕｚｚｙ度量空间一些扩张型映象的不动点定理,这些结果发展和改进了普通度量空间中相应的结果。     

WF-模糊度量空间中的不动点理论

在WF-模糊度量空间中建立压缩型和局部压缩型映射的不动点理论，推广一些重要的不动点定理。     

关于模糊预度量空间中的三角不等式

在L，R为一般三角模时，给出在模糊预一度量空间中三角不等式成立的一个必要条件，并用其给出模糊度量空间的一个不动点定理。     

Fuzzy度量空间扩张型映象的不动点定理

本文给出Ｆｕｚｚｙ度量空间一些扩张型映象的不动点定理,这些结果发展和改进了普通度量空间中相应的结果。     

直觉模糊度量空间上的半群作用

讨论在直觉模糊度量空间上的拓扑半群作用,引入诸如拓扑传递性,点传递性及点稠传递性等概念.考虑非敏感性与传递性,等度连续等动力学性质的相互关系.     

The Comparison Theorem for Bergman and Kobayashi Metrics on Cartan-Hartogs Domain of the Third Type

In this paper, we give the holomorphic sectional curvature under invariant Kähler metric on a Cartan-Hartogs domain of the third type Y _III (N,q,K) and construct an invariant Kähler metric, which is complete and not less than the Bergman metric, such that its holomorphic sectional curvature is bounded above by a negative constant. Hence we obtain a comparison theorem for the Bergman and Kobayashi metrics on Y _III (N,q,K).     

On the metric dimension of HDN

The concept of metric basis is useful for robot navigation. In graph G, a robot is aware of its current location by sending signals to obtain the distances between itself and the landmarks in G. Its position is determined uniquely in G if it knows its distances to sufficiently many landmarks. The metric basis of G is defined as the minimum set of landmarks such that all other vertices in G can be uniquely determined and the metric dimension of G is defined as the cardinality of the minimum set of landmarks. The major contribution of this paper is that we have partly solved the open problem proposed by Manuel et al. [9], by proving that the metric dimension of $\text{HDN1}(n)$ and $\text{HDN2}(n)$ are either 3 or 4. However, the problem of finding the exact metric dimension of HDN networks is still open.     

Common fixed point theorems for some new generalized contractive type mappings

In this paper, some new generalized contractive type conditions for a pair of mappings in metric space are defined. Some common fixed point results for these mappings are presented.     

单值映射对与集值映射对的公共不动点

在度量空间中,引进了单值映射对与集值映射对的调和概念,对调和单值映射对与集值映射对建立了公共不动点定理及相应的随机公共不动点定理。     

局部化单调原理及应用

以下我们总假定(X,d)表度量空间,简记为X,T为X的自映象,B:X?R_+~0=[0,+∞)。我们称X满足广义TCS收敛条件,若存在一点x_0∈X使得{B(T~nx_0)}收敛,蕴含{T~nx_0}有一个收敛子列。称σ(x,T)={x,T_x,T~2x,…,T~nx,…}为x的T轨道。称函数B(x)在p∈X点轨道连续,若{x_n}?σ(x,T),x_n→p,有B(x_n)?B(p)。若B(x)在X内每一点轨道连续,称B(x)在X上轨道连续。我们有如下结果。     

An improved Benders decomposition applied to a multi-layer network design problem

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippel’s previous results.     

A fixed point approach to the stability of functional equations in non-Archimedean metric spaces

In this note, we prove a simple fixed point theorem for a special class of complete metric spaces (namely, complete non-Archimedean metric spaces which are connected with some problems coming from quantum physics, p-adic strings and superstrings). We also show that this theorem is a very efficient and convenient tool for proving the Hyers–Ulam stability of a quite wide class of functional equations in a single variable.     

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. Examples to support our new results are given.