度量空间中反交换映射的公共不动点

本文讨论了度量空间中映射在反交换条件下的公共不动点的存在性问题,给出了映射对在满足一定条件时公共不动点的存在性与唯一性结论.并指出了文献[5]中的几处错误.     

随机积分和微分方程解的存在性准则

在[1]中我们已证明了一个一般的随机不动点定理并给出了某些应用,在本文中我们将给出该结果的进一步应用.首先证明了一随机Darbo不动点定理,然后利用此定理在紧性假设下给出了非线性随机Volterra积分方程和非线性随机微分方程Cauchy问题随机解的存在性准则.我们的定理改进和推广了Lakshmikantham[3,4],Vaugham[2],De Blasi和Myjak[5]等人的结果.     

非线性膨胀型映射的不动点定理

王尚志等在[1]中就B.E.Rhoades在[2]中所归纳出的某些压缩型映射给出了相应的膨胀型映射的定义及不动点定理。本文在此基础上对部分膨胀型映射继续讨论其不动点的存在性,唯一性及不动点集的性质。     

压缩型映象的几个不动点定理

非线性泛函分析中映象的不动点理论,近十多年来有了很大的发展。其中非扩张映象以及各种压缩型映象的不动点理论是讨论得很多的课题。(见[1]—[8]). 本文对现有的结果作一些推广。我们讨论了某些类压缩型映象的性质,并在不必有严格凸性的自反Opial空间,以及不必自反不必严格凸的某类*-Opial空间中,给出了它们的一些不动点定理。另外,我们还讨论了集合值压缩型映象的不动点定理。     

广义Kannan型压缩条件的注记

本文给出了 [4 ]中的广义Kannan型压缩条件下映象的一个不动点定理 ,说明了 [2 5]中广义Kannan型压缩条件下映象与 [1 ]中Kannan型压缩条件下映象具有一致的不动点存在性 .     

一般随机不动点定理及其应用

在本文中我们得到了一个一般的随机不动点定理,推广了Engl[4,7]和Bocsan[8]的主要结果.这一定理的有用性在于目前由许多作者用特殊方法得到的随机不动点定理[1,4,5-13]均能利用我们的一般定理(定理1和系1,2)得到,最后给出了我们的定理对随机积分和微分方程的应用.     

四阶奇异边值问题两个正解的存在性

利用e-范数和锥上的不动点定理,给出了四阶微分方程奇异边值问题两个C2[0,1]和C3[0,1]正解的存在性.     

一个新的不动点定理

<正> 本文在作者工作[1]的基础上,利用Leray-Schauder度理论给出无穷维Banach空间中非线性全连续算子的一个新的不动点定理,此不动点定理把著名的锥拉伸和锥压缩不动点定理中的序关系换成了范数关系,从而具有特点.我们还举例说明了此不动点定理对于Hammerstein积分方程非零解存在性的应用.     

二阶非线性时滞微分方程的多个正解

在这篇文章中,我们探讨了非线性边值问题正解的存在性.给出的主要结果证明了边值问题两个正解的存在性.结论的证明使用了一个锥上的不动点定理.为了说明定理的正确性,我们最后给出了一个例子.     

关于正算子的不动点指数

不动点指数的计算与算子方程解的存在性及算子的固有元的存在性有密切的关系(如参看[4]、[5]、[6]等)。M.A.Krasnosel·skii 在[1]、[2]、[8]中利用“单调下控”的方法,研究了正全连续算子的正固有元的存在性。本文将“单调下控”的思想用于正全连续算子不动点指数的计算,得出正全连续算子的不动点指数为 0 的充分条件,补充了[2]中的有关定理,并顺便得出,一类较线性金连续正算子广的算子在含零点的区域上的不动点指     

On fixpoint objects and gluing constructions

This article has two parts: in the first part, we present some general results about fixpoint objects. The minimal categorical structure required to model soundly the equational type theory which combines higher order recursion and computation types (introduced by Crole and Pitts (1992)) is shown to be precisely a let-category possessing a fixpoint object. Functional completeness for such categories is developed. We also prove that categories with fixpoint operators do not necessarily have a fixpoint object.In the second part, we extend Freyd's gluing construction for cartesian closed categories to cartesian closed let-categories, and observe that this extension does not obviously apply to categories possessing fixpoint objects. We solve this problem by giving a new gluing construction for a limited class of categories with fixpoint objects; this is the main result of the paper. We use this category-theoretic construction to prove a type-theoretic conservative extension result.     

Strong polynomiality of resource constraint propagation

Constraint-based schedulers have been widely successful in tackling complex, disjunctive, and cumulative scheduling applications by combining tree search and constraint propagation. The constraint-propagation step is a fixpoint algorithm that applies pruning operators to tighten the release and due dates of activities using precedence or resource constraints. A variety of pruning operators for resource constraints have been proposed; they are based on edge finding or energetic reasoning and handle a single resource.

Complexity results in this area are only available for a single application of these pruning operators, which is problematic for at least two reasons. On the one hand, the operators are not idempotent, so a single application is rarely sufficient. On the other hand, the operators are not used in isolation but interact with each other. Existing results thus provide a very partial picture of the complexity of propagating resource constraints in constraint-based scheduling.

This paper aims at addressing these limitations. It studies the complexity of applying pruning operators for resource constraints to a fixpoint. In particular, it shows that: (1) the fixpoint of the edge finder for both release and due dates can be reached in strongly polynomial time for disjunctive scheduling; (2) the fixpoint can be reached in strongly polynomial time for updating the release dates or the due dates but not both for the cumulative scheduling; and (3) the fixpoint of “reasonable” energetic operators cannot be reached in strongly polynomial time, even for disjunctive scheduling and even when only the release dates or the due dates are considered.     

Compactness of a fixpoint set and optimal control

Solutions of the dynamic equations in distributed parameter systems are usually obtained as fixpoints of suitable maps, as in Picard iteration. In optimal control of distributed parameter systems, some compactness of the fixpoint set is then needed to extract a convergent minimizing sequence. Two results are obtained to show, when the family of maps is equicontractive, that one can extract such a sequence under suitable hypotheses.     

Generalized Kac-Moody algebras, automorphic forms and Conway's group I

The moonshine properties imply that the twisted denominator identities coming from the action of the monster group on the monster algebra define modular forms. In this paper, we motivate the conjecture that the action of an extension of Conway's simple group Co₁ on the fake monster algebra gives rise to automorphic forms of singular weight on Grassmannians. We prove the conjecture for elements with square-free level and nontrivial fixpoint lattice.     

A useful fixpoint theorem

A sufficient condition for each extensive mapping of an ordered set to have a fixpoint is presented.     

Normalizable linear orders and generic computations in finite models

Numerous results about capturing complexity classes of queries by means of logical languages work for ordered structures only, and deal with non-generic, or order-dependent, queries. Recent attempts to improve the situation by characterizing wide classes of finite models where linear order is definable by certain simple means have not been very promising, as certain commonly believed conjectures were recently refuted (Dawar's Conjecture). We take on another approach that has to do with normalization of a given order (rather than with defining a linear order from scratch). To this end, we show that normalizability of linear order is a strictly weaker condition than definability (say, in the least fixpoint logic), and still allows for extending Immerman-Vardi-style results to generic queries. It seems to be the weakest such condition. We then conjecture that linear order is normalizable in the least fixpoint logic for any finitely axiomatizable class of rigid structures. Truth of this conjecture, which is a strengthened version of Stolboushkin's conjecture, would have the same practical implications as Dawar's Conjecture. Finally, we suggest a series of reductions of the two conjectures to specialized classes of graphs, which we believe should simplify further work. Received: 13 July 1996     

An existence theorem for a type of functional differential equation with infinite delay

Summary We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.     

Existenzsätze für schwach nichtlineare Operatorgleichungen und Anwendung auf Randwertaufgaben mit gewöhnlichen Differentialgleichungen

With Schauder's fixpoint principle we establish an existence theorem for solutions of two simultaneous nonlinear operator equations of the formL _iu=M_iu, i=1,2, L_i linear,M _i continous. By applying this result to boundary value problems with ordinary differential equations we generalize results of Conti and Ehrmann in various directions.