Preservation of Sahlqvist fixed point equations in completions of relativized fixed point Boolean algebras with operators

We define Sahlqvist fixed point equations and relativized fixed point Boolean algebras with operators (relativized fixed point BAOs). We show that every Sahlqvist fixed point equation is preserved under completions of conjugated relativized fixed point BAOs. This extends the result of Givant and Venema (1999) to the setting of relativized fixed point BAOs.     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

广义分散控制系统的无穷远固定模

在控制系统的理论与应用研究中,广义系统、分散系统越来越受到人们的重视.不仅在理论上已有不少有意义的结果,而且这些理论研究有明显的实际背景.例如 Leontief的动态投入产出模型,Leslie 的人口增长模型,电力系统等.然而,在一些实际系统中,系统不仅具有广义性的特点,而且从控制角度来看也具有分散性的特点.因此我们把系统     

New cone fixed point theorems for nonlinear multivalued maps with their applications

In this paper, we first establish some new types of fixed point theorems for nonlinear multivalued maps in cone metric spaces. From those results, we obtain new fixed point theorems for nonlinear multivalued maps in metric spaces and the generalizations of Mizoguchi–Takahashi’s fixed point theorem and Berinde–Berinde’s fixed point theorem. Some applications to the study of metric fixed point theory are given.     

概率度量空间中若干新的不动点定理*

本文提出了Z-M-PN空间的概念,在概率度量空间中我们得到了若干新的不动点定理。同时,一些着名的不动点定理在概率度量空间中得到了推广,诸如:Schauder不动点定理、郭大钧不动点定理和Petryshyn不动点定理被推广到M-PN空间;Altman不动点定理被推广到Z-M-PN空间。     

关于广义分散控制系统无穷远固定模的进一步研究

目前,广义系统的研究已成为控制理论的一个相当活跃的分支.在一些实际系统中,系统不仅具有广义性的特点,而且具有分散性的特点.基于广义系统的这种特点,最近中国科学院的王朝珠、王恩平研究了广义分散控制系统,[1]提出并研究了广义分散控制系统的无穷远固定模,得出了许多出色的结论.本文继续[1]的工作.本文的结论揭示了广义系统无穷远固定模与正常系统分散固定模的内在联系,进而表明一切用来判别分散控制系统固定模的方法均可相应地适用于广义系统无穷远固定模.     

Menger概率度量空间中Caristi型混合不动点定理

本文在Menger概率度量空间中引进Caristi型混合不动点概念,得到两个混合不动点定理和两个集值映象序列的公共混合不动点定理,我们的定理改进和推广了Caristi不动点定理及相关的近期重要结果.     

Generalizations of fixed point theorems and computation

As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets.     

Distortion and stability of the fixed point property for non-expansive mappings

Let X be a Banach space. We say that X satisfies the fixed point property (weak fixed point property) if every non-expansive mapping defined from a convex closed bounded (convex weakly compact) subset of X into itself has a fixed point. We say that X satisfies the stable fixed point property (stable weak fixed point property) if the same is true for every equivalent norm which is close enough to the original one. Denote by P(X) the set formed by all equivalent norms with the topology of the uniform convergence on the unit ball of X. We prove that the subset of P(X) formed by the norms failing the fixed point property is dense in P(X) when X is a non-distortable space which fails the fixed point property. In particular, no renorming of ?₁ can satisfy the stable fixed point property. Furthermore, we show some examples of distortable spaces failing the weak fixed point property, which can be renormed to satisfy the stable weak fixed point property. As a consequence we prove that every separable Banach space can be renormed to satisfy the stable weak fixed point property.     

The fair allocation of common fixed cost or revenue using DEA concept

The common fixed cost or revenue distribution amongst decision making units (briefly, DMUs) in an equitable way is one of the problems that can be solved by data envelopment analysis (DEA) concept. The motivation of this paper is common fixed cost or revenue allocation based on following three principles: First, allocation must be directly proportional to the elements (inputs and outputs) that are directly proportional to imposed common fixed cost or to obtained common fixed revenue. Second, allocation must be inversely proportional to the elements that are inversely proportional to common fixed cost or revenue. Finally, the elements that have no effect on common fixed cost or revenue must have no effect on allocation as well.     

Generalized KKM theorems and common fixed point theorems

In this paper, we first prove a generalized KKM theorem, and then use this generalized KKM theorem to establish the generalized equi-KKM theorem, common fixed point theorems for a family of multivalued maps, and the Kakutani-Fan-Glicksberg fixed point theorem. We also show that an existence theorem of the common fixed point theorem is equivalent to the Kakutani-Fan-Glicksberg fixed point theorem.     

我国固定资产投资边际效率问题研究

将回归分析与边际效用理论有机结合,深入研究我国固定资产投资对GDP边际贡献问题.研究结果表明在整个正实数区间内高技术产业固定资产投资对GDP边际贡献高于全社会固定资产投资和城镇房地产开发固定资产投资对GDP边际贡献;在0～349578.8207亿元投资区间内,城镇房地产开发固定资产投资对GDP边际贡献高于全社会固定资产投资边际贡献平均水平;当投资额度大于349578.8207亿元时,城镇房地产开发固定资产投资对GDP边际贡献小于全社会固定资产投资边际贡献平均水平.研究结果印证了科技是第一生产力的论断,同时也与我国当前控制房地产开发投入、鼓励发展高新技术产业等宏观经济政策相吻合.     

Remarks on Caristi’s fixed point theorem and Kirk’s problem

Without assumptions on the continuity and the subadditivity of η, by means of Caristi’s fixed point theorem, we investigated the existence of fixed points for a Caristi type mapping which partially answered Kirk’s problem and improved Caristi’s fixed point theorem, Jachymski’s fixed point theorem and Khamsi’s fixed point theorem since φ is not necessarily assumed to be bounded below on X.     

Construction of a fixed point for contractions in Banach space

A method for constructing fixed points of contractions in uniformly convex Banach spaces is developed. The fixed point obtained is the limit of one sequence that always converges (provided that a fixed point exists).     

Forbidden retracts for finite ordered sets of width at most four

The relationship between the fixed point property and forbidden retracts associated with a forgetful functor is formulated. Finite ordered sets of width at most four with fixed point free automorphisms are described. Linear time algorithms for deciding whether a finite ordered set of width two has the fixed point property and whether a finite ordered set of width at most three has a fixed point free automorphism are presented.     

Lattices of Fixed Points of Fuzzy Galois Connections

We give a characterization of the fixed points and of the lattices of fixed points of fuzzy Galois connections. It is shown that fixed points are naturally interpreted as concepts in the sense of traditional logic.     

COUPLED FIXED POINTS OF SKEW INCREASING OPERATORS AND APPLICATIONS

1Intr0ducti0nIllthisPaPerwestudythefordpointsandcouPledfiXedpointsofskewincreasing0PeratorsandtheiraPplicaion.LetXbeaBanachsPaCcwithapartialorderingintr0ducedbythcc0neK-LctF:X-Xbean0peraorinX.FiscaJledinCreasingifF2SFgf0raJl2Sy.Asiswellkllown,inthetheorerns0fhapointforincreasingoPerbo,thereisaninterestinginterreboi0nbetweenPr0pertiesofKandF,thatisThoorem1l1I'I2ILetXbeaBanachpee,partiaJlyorderedbythecolleKGX.Let[a,b]beanordeintervalandF:[a,b]- [a,b]increasin.ThenFhasabop0intif0…     

多项式不动点的进一步研究

对文[1]中关于多项式不动点的主要定理进行了修正和发展,进而研究了多项式的广义(高阶)不动点,证明了对任意给定的n个点t_1≤t_2≤…≤t_n,存在唯一的首项系数为α∈R(α≠0)的n次多项式P(x)以它们为广义不动点.     

Fixed points of analytic self-mappings of Riemann surfaces

The existence of fixed points for an analytic self-mapping of a Riemann surface often permits strong conclusions about the mapping. For hyperbolic Riemann surfaces fixed point conditions that imply an analytic self-mapping is actually a conformal automorphism are given. For instance, an analytic self-mapping of a hyperbolic Riemann surface with two fixed points must be a conformal automorphism of finite order. On the other hand, for surfaces of finite genus estimates of the order of a conformal automorphism are obtained from fixed point information. For example, on a Riemann surface of genus g a conformal automorphism with 2g+3 fixed points is the identity.     

The Split Common Fixed Point Problem for Directed Operators

We propose the split common fixed point problem that requires to find a common fixed point of a family of operators in one space whose image under a linear transformation is a common fixed point of another family of operators in the image space. We formulate and analyze a parallel algorithm for solving this split common fixed point problem for the class of directed operators and note how it unifies and generalizes previously discussed problems and algorithms.