Fixed points for some non-obviously contractive operators

The use of K-normed spaces gives us the possibility to prove that a fixed point theorem due to B. Luo is equivalent to the Banach Contraction Principle. This confirms the conspiracy among fixed point theorems. Moreover the theorem of Lou is improved and extended to different contexts. A counterexample about the fixed points of the sum of a contraction and an integral operator is given. The usefulness of K-norm is tested on a Volterra integral equation as well.

     

The Degree Theory of a New Operator

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｄｅｇｒｅｅｔｈｅｏｒｙｆｏｒａｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｏｐｅｒａｔｏｒｈａｓｍａｎｙａｐｐｌｉｃａｔｉｏｎｓｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｓｏｍｅｅｑｕａｔｉｏｎｓ（ｓｅｅ［１］，［２］，［３］）．Ｈｏｗｅｖｅｒ，ｓｏｍｅｏｐｅｒａ－ｔｏｒｓａｒｅｎｏｔｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｏｐｅｒａｔｏｒｓ．Ｉｔｉｓａｎｅｗｐｒｏｂｌｅｍｔｈａｔｗｅｅｓｔａｂｌｉｓｈａｄｅｇｒｅｅｔｈｅｏｒｙｆｏ…     

A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM

This paper represents an inexact sequential quadratic programming (SQP) algorithm which can solve nonlinear programming (NLP) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.     

Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces

Set-valued weaker contractions in uniform, locally convex and metric spaces are defined and dynamic systems of such weaker contractions are studied. Conditions guaranteeing the convergence of generalized sequences of random iterations and iterations and the existence and uniqueness of endpoints of set-valued weaker contractions are established. Our definitions and results are new for set-valued maps in uniform, locally convex and metric spaces and even for single-valued maps.     

KKM property and fixed point theorems in metric spaces

In this paper, first part, we establish some fixed point theorems for a k-set contraction map on the nearly-subadmissible subsets of a complete metric space. The second part, we deduce a generalization of the approximate fixed point theorem for the lower semicontinuous mappings on a metric space.     

原子核内的夸克分布：Ⅱ 原子核的遮掩效应

本文讨论了原子核遮掩效应对EMC效应可能的贡献.根据众多的实验数据构造了一个能较好地描述遮掩效应的唯象关系,这一关系与通常人们表述遮掩效应的方法不同,是用通常结构函数的变量来表示的.     

A concise synthetic pathway towards 5-substituted indolizidines

The total synthesis of 5-(2′-hydroxyethyl)indolizidine via 5-thioindolizidinone is described. The key step is the transformation of 5-thioindolizidinone via Eschenmoser’s sulfide contraction. The racemic mixture of 5R,9R- and 5S,9S-5-(2′-hydroxyethyl)indolizidine was obtained in seven steps in 17% overall yield from 2-allyl cyclopentanone.     

集值渐近非扩张型映射的不动点定理

本文首先给出了集值渐近非扩张(型)映射的概念,在Hilbert空间中证明了连续集值渐近非扩张型映射的遍历收敛性定理。     

T‐joins intersecting small edge‐cuts in graphs

In an earlier paper 3 , we studied cycles in graphs that intersect all edge‐cuts of prescribed sizes. Passing to a more general setting, we examine the existence of T‐joins in grafts that intersect all edge‐cuts whose size is in a given set A ?{1,2,3}. In particular, we characterize all the contraction‐minimal grafts admitting no T‐joins that intersect all edge‐cuts of size 1 and 2. We also show that every 3‐edge‐connected graft admits a T‐join intersecting all 3‐edge‐cuts. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 64–71, 2007