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1.
在Hilbert空间与可分Banach空间关于随机级数的收缩原理   总被引:3,自引:1,他引:2  
田范基 《数学杂志》1997,17(4):433-435
在Hilbert空间与可分Banach空间,用独立随机元收敛准则或三级数定理的思想,证明了关于随机级数的民上缩原理。  相似文献
2.
Banach压缩映象原理与空间完备性   总被引:3,自引:0,他引:3       下载免费PDF全文
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  相似文献
3.
An Extension of the Contraction Principle   总被引:1,自引:1,他引:0  
The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large deviations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its transform (via an almost compact function) is studied here in metric spaces. Counterexamples are given to the nonmetric case. Relations between almost compactness of a function and the goodness of a rate function are studied. Applications of the main theorem are given, including to an approximation of the stochastic integral.  相似文献
4.
In this paper, we study a boundary value problem of nonlinear fractional differential equations of order q (1 < q ≤ 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.  相似文献
5.
We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem.

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6.
If is a complete metric space and is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader mappings.

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7.
The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.  相似文献
8.
利用压缩映射原理,讨论了非线性中立型差分方程正解的存在性.  相似文献
9.
本文利用Banach压缩映射原理,讨论了中立型时滞脉冲微分方程正解的存在性。  相似文献
10.
We introduce the notion of -continuity, which generalizes both continuity and the hypothesis in the Generalized Banach Contraction Conjecture, and prove that any -continuous self-map on a scattered compact space, has an invariant finite set. We use the results and the techniques to prove the Generalized Banach Contraction Conjecture.

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