Banach压缩映象原理与空间完备性

本文进一步揭示了Ｂａｎａｃｈ压缩映象原理与完备性的关系，指出：一般地，Ｂａｎａｃｈ压缩映象原理等价于道路完备性，在一定条件下才等价于完备性，进一步给出了这一等价性成立的充要条件     

梯度度量空间中的Banach压缩映像原理

利用梯度数引入梯度度量空间的概念,证明了一个梯度赋范线性空间可以诱导一个梯度度量空间.在完备的梯度度量空间框架下,给出了相应的Banach压缩映像原理,并且用实例说明了其合理性.     

Simple proof of a large deviation result

In this note we prove the large deviation principle for the following process in R:dxt = b(xt, t)dt edwt, t E [0, 1], (1)where the initial point xo is fixed, wt is a Wiener process5 E > 0 is a small parameter whichtends to 0, b(x, t) is a bounded piecewise Lipschitz function of the form(b (x, t), x > 0t,b(xlt)={b--(::t)i x<0jf (2)where e is a smooth curve, bf are two bounded Lipschitz functions on (--oo, co) x [0, oo)satisfyingb--(0t, t) 2 b (0t, t). (3)If (3) is replaced with an opposite …     

严格集压缩映射和凝聚映射的延拓定理及应用(英文)

应用著名的Dugundji延拓定理和Urysohn引理,将Hilbert空间E中有界闭凸集D上的k-集压缩映射和聚映射延拓到全空间,并给出了其在拓扑度计算方面的应用.     

一般扩展原理

本文中称Ｚａｄｅｈ（１９７５）给出的扩展原理为极大扩展原理，我们给出了一个极小扩展原理，并研究了它的一些基本性质。之后，建立了一般扩展原理的公理化结构，并给出了几种具体结构形式，为近似推理和信息分析提供了有效的工具。     

An Extension Principle for Fuzzy Logics

Let S be a set, P(S) the class of all subsets of S and F(S) the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P(S) into a fuzzy closure operator J* defined in F(S). This enables us to give the notion of canonical extension of a deduction system and to give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. Mathematics Subject Classification : 03B52.     

Fuzzy压缩原理

本文给出以Ｆｕｚｚｙ数作为Ｌｉｐｓｃｈｉｔｚ常数的压缩映射的新概念，并成功证明了Ｆｕｚｚｙ数值函数的不动点定理。     

Extensions of Banach's Contraction Principle

Let A and B be nonempty subsets of a metric space. As a non-self mapping T: A → B does not necessarily have a fixed point, it is of considerable interest to find an element x that is as close to Tx as possible. In other words, if the fixed point equation Tx = x has no exact solution, then it is contemplated to find an approximate solution x such that the error d(x, Tx) is minimum. Indeed, best proximity point theorems investigate the existence of such optimal approximate solutions, called best proximity points, of the fixed point equation Tx = x when there is no exact solution. As d(x, Tx) is at least d(A, B), a best proximity point theorem achieves an absolute minimum of the error d(x, Tx) by stipulating an approximate solution x of the fixed point equation Tx = x to satisfy the condition that d(x, Tx) = d(A, B). This article furnishes extensions of Banach's contraction principle to the case of non-self mappings. On account of the preceding argument, the proposed generalizations are formulated as best proximity point theorems for non-self contractions.     

An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1].