Banach空间中ψ-半压缩型映象不动点的迭代逼近

设X为实一致光滑Banach空间,K为X的非空凸子集满足K+KK.设T：K→K为有界ψ-半压缩映象.设{vn｝∞n=0｛vn｝∞n=0为K中的序列,{αn｝∞n=0,{βn}∞n=0为[0,1]中的实数列满足 　　(i) 　　(ii)αn→0,βn→0,n→∞ 　　(iii) 　　对任意初值x0∈K,定义Ishikawa迭代序列{xn｝∞n=0如下： 　　 　　若｛Tyn｝有界,则｛xn｝强收敛于T的唯一不动点.由此导出一些相关的结果.     

Banach空间中关于Lipschitz φ-半压缩映象的带误差项的Ishikawa迭代过程

本文在任意Ｂａｎａｃｈ空间中研究了Ｌｉｐｓｃｈｉｔｚ φ－半压缩映象与φ－强拟增生映象的带误差项的Ｉｓｈｉｋａｗａ迭代过程,使用新的分析技巧建立了几个强收敛定理．     

真拟弱几乎周期点和拟正则点

T为紧致度量空间X上的连续映射,M（X）为X上所有Borel概率测度.设x∈X,记Mx（T）为概率测度序列{1n∑n 1i=0δTi（x）}在M（X）中的极限点的集合,其中δx表示支撑集是{x}的点测度.记W（T）和QW（T）分别为T的弱几乎周期点和拟弱几乎周期点集.本文证明,如果（X,T）非平凡且满足specifcation性质,则存在x,y∈QW（T）／W（T）（称为真拟弱几乎周期点）,分别满足μ∈Mx（T）,x∈Supp（μ）和ν∈My（T）,y∈/Supp（ν）,回答了周作领等提出的公开问题.Mx（T）在弱拓扑中是紧致连通集,所以,要么是单点集,要么是不可数集.如果x∈QW（T）／W（T）,则Mx（T）是不可数集.一个自然的问题是,怎么刻画M x（T）是单点集的点x（这时x称为拟正则点）.本文给出M x（T）是单点集的充要条件.     

A criterion of vanishing of the spectral density based on homoclinic sums

Let (X, d) be a compact metric space, let T: X→X be a homeomorphism satisfying a certain suitable hyperbolicity assumption, and let μ be a Gibbs measure on X relative to T. Let λ be a complex number |λ|=1, and let f:X → ? be a Hölder continuous function. It is proved that $\sum\limits_{k \in \mathbb{Z}} {\lambda ^{ - k} } \left( {\int\limits_X {f(T^k x)\bar f(x)\mu (dx) - \left| {\int\limits_X {f(x)\mu (dx)} } \right|^2 } } \right) = 0$ if and only if ∑λ^?k(f(T^ky) ? f(T^kx)) = 0 for all x, y ε X such that $d(T^k x,T^k y)\xrightarrow[{|k| \to \infty }]{}0$ . Bibliography: 11 titles.     

Zeros of accretive operators

In the investigation of accretive operators in Banach spaces X, the existence of zeros plays an important role, since it yields surjectivity results as well as fixed point theorems for operators S such that I-S is accretive. Let D?X and T: D→X an operator such that the initial value problems (1) u′(t)=-Tu(t), u(0)=x εD are solvable. Then T has a zero iff (1) has a constant solution for some xεD. Under certain assumptions on D and T it is possible to show that (1) has a unique solution u(t,x) on [0,∞), for every xεD. In this case, define U(t): D→D by U(t)x=u(t,x). If T is accretive it turns out that U(t) is nonexpansive for every t≥0. This fact constitutes the basis for several authors concerned with this subject. They proceed with assumptions on D and X ensuring either that the U(t) must have a common fixed point x_o or that U(_p) has a fixed point x_p for every p≥0. In the first case, U(t)x_o is a constant solution of (1), whence Tx_o=0. In the second case, U(t)x_p is a p-periodic solution of (1). Hence, one has to impose additional conditions on T which imply that a p-periodic solution must be constant, for some p>0. The main purpose of the present paper is to show that, in certain situations, either the operators U(t) are actually strict contractions or T may be approximated by operators T_n such that the corresponding U_n(t) are strict contractions. Thus, we obtain several results in general Banach spaces and a unification of some results in special spaces.     

关于增生算子方程的具误差的Ishikawa迭代序列的收敛率估计

设X是一实的Banach空间,TLX→X是—Lipschitz的增生算子;证明了具误差的Ishikawa迭代序列强收敛到x＋Tx=f的唯一解;得到一个一般的收敛率估计式．进一步得到：若了T：X→X是—Lipschitz的强增生算子,则具误差的Ishikawa迭代序列强收敛到Tx=f的唯一解．文中结果推广和发展了已有的相关结果．     

关于A-收敛

设A={ai}（i=1）∞S_（e_1）~＋,其中S（e1）＋={x=（x（n））∈e1：‖x‖=1且x（n）≥0对任意的n∈N}.Banach空间X中的序列{x_n}称为A-收敛于x∈X是指对任意的ε〉0,→0当i→∞,其中A（ε）={n∈N：‖x_n-x‖≥ε}.这篇文章中,我们证明了该收敛可以用一个有限可加的概率测度加以刻画.我们对A-收敛与统计收敛的关系进行了讨论,证明了A-收敛为统计收敛完全取决于A的w~＊-拓扑性质.     

关于渐近伪压缩映象迭代逼近的表征

设C是Banach空间X的非空有界闭凸子集,T:C →C既是一致L-Lipschitz映象, L≥1,又是渐近伪压缩映象,具有序列{kn}(?)[1,∞),limn→kn=1.固定u∈C.对每个n≥1,xn是压缩映象Sn(x)=(1-(tn)/(Lkn))u (tn)/(Lkn)Tnx, (?)x∈C的唯一不动点,其中,{tn}(?) [0,1). 在适当的条件下,本文表征了序列{xn}强收敛到T的不动点.     

回归函数改良核估计的渐近分布

设(X1,Y1),…,(Xn,Yn)是来自二元总体(X,Y)的样本,若EY＜∞,则回归函数m(x)＝E(Y｜X＝x)存在。在本文中,考虑m(x)的改良核估计     

一类连续体上连续映射的周期点

设X是个阶有限的遗传可分解可链连续体, f:X→X是X上的连续自映射, On(x,f)={fi(x):0≤i≤n)是f的一个返回轨道, inf(On(x,f))相似文献   

非扩张映象不动点的迭代算法

设C是具有一致Gateaux可微范数的实Banach空间X中的一非空闭凸子集,T是C中不动点集F(T)≠0的一自映象．假设当t→0时,{Xt}强收敛到T的一不动点z,其中xt是C中满足对任给u∈C,xt=tu+(1-t)Txt的唯一确定元．设{αn},{βn}和{γn}是[0,1]中满足下列条件的三个实数列:(i)αn+βn+γn=1;(ii) limn-∞αn=0和．对任意的x0∈C,设序列{xn}定义为xn+1=αnu+βnxn+γnTxn,则{xn}强收敛到T的不动点．     

强向量拟均衡问题解的存在性(英文)

设X是一个实的Hausdorff拓扑向量空间,Y是一个实的局部凸向量空间,C是Y中的闭凸锥,K（?）X是一个紧子集.F:X×X→Y是一个双向量函数,G:K→2K是一个集合值映射.我们考虑下面的强拟均衡问题:存在x∈G（x）,使得对任意的y∈G（x）,成立F（x,y）∈C.本文证明了当F是半连续时,上述问题解的存在性结论.     

赋范空间中Lipschitz Φ-半压缩映象不动点的迭代逼近

设X为赋范线性空间,K为X的非空凸子集,T:K→K为LipschitzΦ-半压缩映象.设{αn}n∞=0和{βn}n∞=0为[0,1]中的实数列且满足一定条件.则Ishikawa迭代序列{xn}n∞=0强收敛于T的唯一不动点.结果完整地回答了周海云提出的公开问题.     

變敍的項的共同分佈的極限

<正> 合X為一隨機变數,其分佈律為F(x).今對X作n次相互獨立的觀察,便得n個值,把這n個值依其大小順序排列為     

求0~0型极限在弱条件下的简便方法

利用洛必达法则与等价无穷小代换对抽象函数的00型极限可得结论:设当x→x0时f(x)与g(x)为无穷小,g(x)～(x-x0)β,取k为正实数,使得fk(x)=A(x-x0)α+o[(x-x0)α],其中A0,α≥2,β0为实数,则有limx→x0f(x)g(x)=1.该方法对求常见的00型极限都适用.当使用洛必达法则求li mx→x0f(x)g(x)很复杂时,使用该方法可简化计算.     

Division and k-th root theorems for Q-manifolds

We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f:K→X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X2 and X×[0,1] are Q-manifolds as well. We construct a countable familyχof spaces with DDP and cd-AP such that no space X∈χis homeomorphic to the Hilbert cube Q whereas the product X×Y of any different spaces X, Y∈χis homeomorphic to Q. We also show that no uncountable familyχwith such properties exists.     

EXISTENCE PROBLEMS OF ADDITIVE SELECTION MAPS FOR ANOTHER TYPE SUBADDITIVE SET-VALUED MAP

In this paper,we consider the following subadditive set-valued map F:X → P 0 (Y):F r ∑ i=1 x i + s ∑ j=1 x r+ j rF r ∑ i=1 x i r + sF s ∑ j=1 x r+ j s, x i ∈ X,i=1,2,,r + s,where r and s are two natural numbers.And we discuss the existence and unique problem of additive selection maps for the above set-valued map.     

Verallgemeinerungen eines Satzes von H. Steinhaus

The following result is due to H. Steinhaus [20]: “If A,B?R are sets of positive inner Lebesgue measure and if the function f: R x R→R is defined by f(x,y):=x+y (x,y?R), then the interior of f(A x B) is non void”. In this note there is proved, that the theorem of H. Steinhaus remains valid, if

1. R is replaced by certain topological measure spaces X, Y and a Hausdorff space Z,
2. f is a continuous function from an open set T?X x Y into Z and satisfies a special local (respectively global) solvability condition in T,
3. A?X is a set of positive outer measure, B?Y contains a set of positive measure and A x B?T.

     

关于一致凸Banach空间中渐近非扩张半群的几乎轨道的渐近行为

设Ｘ是具有Ｆｒｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｓ＝｛Ｔ（ｔ）：ｔ≥０｝是Ｃ上渐近非扩张牛群．若ｕ（·）：［０，＋∞）→Ｃ是Ｓ的几乎轨道且关于ｔ∈［０，＋∞）一致连续，则｛ｕ（ｔ）｝几乎弱收敛到集合　　｛ｕ（ｒ）：ｒ≥ｔ｝∩Ｆ（ｓ）的唯一点。     

An existence-convergence theorem for a class of iterative methods

LetM ₀, characterized byx _k+1=G ₀(x _k),k?0,x ₀ prescribed, be an iterative method for the solution of the operator equationF(x)=0, whereF:X → X is a given operator andX is a Banach space. Let ω:X → X be a given operator, and let the methodM _mbe characterized byx _x+1,m =G _m(x _k,m),k?0,x _0,m prescribed, where $$G_i (x) = G_0 (x) - \sum\limits_{j = 0}^{i - 1} { F'(\omega (x))^{ - 1} F(G_j (x)), i = 1, . . . ,m,} $$ in whichG ₀:X → X is a given operator andF′:X → L(X) is the Fréchet derivative ofF. Sufficient conditions for the existence of a solutionx* _m ofF(x)=0 to which the sequence (x _k,m) generated from methodM _mconverges are given, together with a rate-of-convergence estimate.