On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

凝聚映射的凝聚延拓及其多重不动点

1 引言 R.W.Leggett和L.R.William[1]在Banach空间E的正锥上给出全连续算子A有两个,或有三个不动点的充分条件。本文主要结果是给出凝聚映射A的几个凝聚延拓公式。并把[1]中全连续算子的几个定理推广到凝聚映射。     

一类非紧算子的不动点

运用Zorn引理得到了非紧，非单调算子不动点存在性的一些有趣结果。     

局部FC-空间上的几乎不动点和不动点

利用古典的KKM原理的开[闭]形式得到FC-空间上的KKM型定理并给出局部FC-空间上的上[下]半连续映射的几乎不动点定理,最后给出在局部FC-空间上具有闭值且其值为FC-子空间的上半连续映射的不动点定理.     

一个多值增算子的不动点定理

研究了一个多值增算子的不动点问题,获得了几个存在性定理,所获结果推广了已知的结论.     

Fixed Points for Mean Non-expansive Mappings

For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.     

集值1—集压缩映象的重合点与不动点

本文在Banach空间中,证明了集值l—集压缩映象对的重合点定理与集值l—集压缩映象列的公共不动点定理.     

Meir-Keeler Type Contractions for Tripled Fixed Points

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.     

扭转映射的一个不动点定理

本文利用集连通理论，给出了非保面积的扭转映射至少有两个不动点的一个新定理．     

Inequalities for Fixed Points of Holomorphic Functions

Cowen and Pommerenke obtained inequalities for fixed pointsof holomorphic and univalent functions in [1]. There was onlyone case where their inequality was not the best possible. Byan entirely new method, we will establish a sharp improvementto this case and provide simple proofs to their main resultsin [1]     

Lower Bounds for Fixed Spectrum Frequency Assignment

Determining lower bounds for the sum of weighted constraint violations in fixed spectrum frequency assignment problems is important in order to evaluate the performance of heuristic algorithms. It is well known that, when adopting a binary constraints model, clique and near-clique subproblems have a dominant role in the theory of lower bounds for minimum span problems. In this paper we highlight their importance for fixed spectrum problems. We present a method based on the linear relaxation of an integer programming formulation of the problem, reinforced with constraints derived from clique-like subproblems. The results obtained are encouraging both in terms of quality and in terms of computation time.     

Computational Complexity of Fixed Points and Intersection Points

We study the computational complexity of Brouwer′s fixed point theorem and the intersection point theorem in the two-dimensional case. Papadimitriou (1990, in "Proceedings, 31st IEEE Sympos. Found. Comput. Sci.," pp. 794-801) defined a complexity class PDLF to characterize the complexity of the fixed point theorem in the three-dimensional case. We define a subclass PMLF of PDLF and show that the fixed points and the intersection points of polynomial-time computable functions are not polynomial-time computable if PMLF contains a function on unary inputs that is not polynomial-time computable.     

映射F_p:X→‖AXB-C‖_p~p的临界点的特征

对于Ｈｉｌｂｅｒｔ空间上有界线性算子Ａ、Ｂ、Ｃ,考虑了当Ａ有一个广义逆Ａ~－使得（ＡＡ~－）~＊＝ＡＡ~－,Ｂ有一个广义逆 Ｂ~－使得（Ｂ~－ Ｂ）～＊＝ Ｂ~－ Ｂ时,映射 Ｆ_ｐ： Ｘ→｜｜ＡＸＢ－ Ｃ｜｜_ｐ~ｐ临界点的特征的一般形式（１＜ ｐ＜∞）,推广了Ｐ．Ｊ．Ｍａｈａｒ的关于对ｐ＝ ２时的结果,并指出该定理可推广到多个算子的情形．     

局部熵高维重分形谱的上界估计

We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.     

Generic Existence of Fixed Points for Set-Valued Mappings

We first consider a complete metric space of nonexpansive set-valued mappings acting on a closed convex subset of a Banach space with a nonempty interior, and show that a generic mapping in this space has a fixed point. We then establish analogous results for two complete metric spaces of set-valued mappings with convex graphs.     

On Essential Sets of Fixed Points for Functions

This article studies essential stabilities of fixed points under the dual perturbations of functions and domains using uniform topology. We show that each fixed point for most functions has the ability to resist these dual perturbations. The existence result of minimal essential sets of fixed points is established, and the connectedness of minimal essential sets is proved under some conditions. These generalize some corresponding results in references.     

有关不连续随机增算子的随机不动点

本文利用Zorn引理和锥理论,研究了不连续随机算子的随机不动点的存在性问题,得到了几个有关不连续随机增算子的随机不动点定理.