Affine and Projective Tree Metric Theorems

The tree metric theorem provides a combinatorial four-point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A related weaker four point condition characterizes dissimilarity maps derived from circular split systems known as Kalmanson metrics. The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics, and Robinsonian matrices, and the theorems that relate them. As with tree metrics and ultrametrics, the link between PC-trees and PQ-trees is established via the Gromov product.     

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.     

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-Spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.     

PM-空间中混合压缩的不动点定理与重合点定理

引进了Menger PM-空间中多值情形下的相容映象和弱相容映象概念,并研究了二者之间的联系．在此基础上,获得了Menger PM-空间中若干新的不动点和重合点定理．最后,给出了这一结果在度量空间中的应用．     

FC-空间上的不动点定理和相交定理及其应用

介绍了没有凸结构和线性结构的有限连续拓扑空间(简称为FC-空间);得到了若干个非紧的FC-空间上不动点定理的开[闭]表现形式并建立了FC-空间上的连续选择定理.应用以上结果,在非常弱的假设下得出若干的相交定理和重合点定理,改进和推广了文献中的相应结果.     

Heterogeneous Vectorial Fixed Point Theorems

In this paper, we obtain fixed point theorems for operators defined on Cartesian product spaces under heterogeneous conditions upon the structure of the factor spaces and the operator components. The main results combine Banach–Perov contraction principle with topological fixed point theorems of Mönch type in strong and weak topologies. The results make possible a tinted analysis of the operator systems. An application of the vectorial technique to evolution equations with nonlocal Cauchy conditions is included.     

Partial b-Metric Spaces and Fixed Point Theorems

The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.     

Fixed Point Theorems and Convergence Theorems for a New Generalized Nonexpansive Mapping

Abstract

This paper introduces a new mapping that is weaker than nonexpansive mapping. The new mapping is different from the Suzuki’s generalized nonexpansive mapping. This paper introduces a new iteration process for the fixed point, and gives fixed point theorems and Convergence theorems for a new generalized nonexpansive mapping in Banach space, insteading of uniformly convex Banach space.     

FC-空间中的不动点定理定理及应用

在FC-空间中建立了一个不动点定理,推广了近期文献的一个相关结论利用这个结果,我们建立了一些广义型定理,推广了著名的截口定理到FC-空间中借助这个截口定理,在FC-空间得到一些新的广义向量均衡问题解的存在性定理.     

On Tverberg partitions

A theorem of Tverberg from 1966 asserts that every set X ? ? ^d of n = T(d, r) = (d + 1)(r ? 1) + 1 points can be partitioned into r pairwise disjoint subsets, whose convex hulls have a point in common. Thus every such partition induces an integer partition of n into r parts (that is, r integers a ₁,..., a _r satisfying n = a ₁ + ··· + a _r ), in which the parts a _i correspond to the number of points in every subset. In this paper, we prove that for any partition of n where the parts satisfy a _i ≤ d + 1 for all i = 1,..., r, there exists a set X ? ? of n points, such that every Tverberg partition of X induces the same partition on n, given by the parts a ₁,..., a _r .     

Common Fixed Point Theorems in Topological Vector Spaces via Intersection Theorems

Our purpose in this paper is to present two methods for obtaining common fixed point theorems in topological vector spaces. Both methods combine an intersection theorem and a fixed point theorem, but the order in which they are applied differs.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

Generalized Probabilistic Metric Spaces and Fixed Point Theorems

Several results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces.     

非紧非单调算子的不动点定理

本文利用和选择公理等价的Zorn引理,得到了一般非单调算子不动点存在性的一些结果.     

几个不动点定理及其应用

得到凝聚映象的几个新的不动点定理 ,并用到一类非线性积分方程的非零解、正解和解的性状的研究上得出了新的结果 .     

L-空间中的KKM映射及不动点定理

引入了L-空间和L-空间上的KKM类映射,建立了关于该类映射的一些不动点定理,其中包括Schauder型和Fan-Browder型不动点定理．得到了L-空间中的KyFan匹配定理和叠合点定理．     

Fixed Point Theorems for Non-convex Valued Multifunctions

The purpose of this paper is to establish fixed point theorems for non-convex valued multifunctions which generalize known results in the literature. We also derive coincidence theorems in the non-compact setting.AMS Subject Classification (2000): 47H, 54H     

CARISTI型Fuzzy混合不动点定理

本文提出ｆｕｚｚｙ混合不动点的概念，给出两个ｆｕｚｙ混合不动点定理和两个ｆｕｚｙ映象序列的公共ｆｕｚｚｙ混合不动点定理．本文的结果改进和推广了Ｃａｒｉｓｔｉ不动点定理及其近期的重要推广