Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

A THEOREM OF UNIFORMLY ASYMPTOTIC STABILITY FOR DELAY DIFFERENCE SYSTEM

In this paper, we establish a criterion of unformly asymptotic stability for finite delay difference systems in terms of two measures by employing Lyapunov functionals method.     

Wijsman and Hit-and-Miss Topologies of Quasi-Metric Spaces

The relationship between the Wijsman topology and (proximal) hit-and-miss topologies is studied in the realm of quasi-metric spaces. We establish the equivalence between these hypertopologies in terms of Urysohn families of sets. Our results generalize well-known theorems and provide easier proofs. In particular, we prove that for a quasi-pseudo-metrizable space (X,T) the Vietoris topology on the set P ₀(X) of all nonempty subsets of X is the supremum of all Wijsman topologies associated with quasi-pseudo-metrics compatible with T. We also show that for a quasi-pseudo-metric space (X,d) the Hausdorff extended quasi-pseudo-metric is compatible with the Wijsman topology on P ₀(X) if and only if d ^–1 is hereditarily precompact.     

模糊化的Egoroff定理

在一般模糊测度空间上,针对可测模糊值函数序列给出了几乎处处收敛,几乎一致收敛和伪几乎一致收敛的概念,并在此基础上,进一步研究了这几种收敛的蕴涵关系,从而获得了模糊化的Egoroff定理,使模糊值函数序列的理论得到进一步丰富.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

有限个渐近伪压缩映射近迫点序列的收敛性

研究了Banach空间中有限个渐近伪压缩映射近迫点序列的收敛性问题,此结果推广了以前的结论.     

污染分布的近邻估计

本文研究了污染分布中污染系数和未知主体分布密度的估计问题.利用近邻估计法得到了它们的估计量,并且证明了此估计量均满足一致弱相合性,同时对污染系数的估计进行了统计模拟,并与用核密度估计得出的结果作比较.结果显示估计的好坏与样本量的多少和参数的选取有关.     

A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations

This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations.     

Banach空间中Mann迭代和Ishikawa迭代的等价性问题

用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{βn}仅需lim sup n→∞βn〈k/L（L＋1）,这推广和改进了目前需假设lim n→∞ βn=0和两迭代程序初始点的取值需相同条件下的已有结果.