Banach空间非扩张映像不动点强收敛定理

设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点.     

渐近非扩张非自映射的收敛定理(英文)

设E是实的一致凸Banach空间,K是E的一个非空闭凸集,P是E到K上的非扩张的保核收缩映射.设T1,T2,T3:K→E分别是具有数列{hn},{ln},{kn}[1,∞)的渐近非扩张非自映射,使得sum (hn-1) from n=1 to ∞<∞,sum ((ln-1)) from n=1 to ∞<∞及sum (n=1(kn-1) from n=1 to ∞<∞,且F=F(T1)∩F(T2)∩F(T3)={x∈K:T1x=T2x=T3x}≠Ф.定义迭代序列{xn}:x1∈K,xn+1=P((1-αn)xn+αnT1(PT1)n-1yn),yn=P((1-βn)xn+βnT2(PT2)n-1zn),zn=P((1-γn)xn+γnT3(PT3)n-1xn),其中{αn},{βn},{γn}[ε,1-ε],ε是大于零的实数.(i)如果T1,T2,T3中有一个是全连续的或者半紧的,则{xn}强收敛于某一点q∈F;(ii)如果E具有Frechet可微范数或者满足Opial’s条件或者E的对偶空间E~*具有Kadec-Klee性质,则{xn}弱收敛于某一点q∈F.     

有限个非扩张非自映像隐迭代格式的逼近

假设E为一致凸Banach空间,K为E的非空闭凸子集且为E的非扩张收缩,P为非扩张收缩映像.{Ti:i=1,2,…,N}:K→E为非扩张映像且F(T)=∩ from i=1 to N F(Ti)≠■.定义{xn}如下:x0∈K,xn=P(αnxn-1+(1-αn)TnP[βnxn-1+(1-βn)Tnxn]),n≥1,这里{αn},{βn}为[δ,1-δ]中的实序列,其中δ∈(0,1).若{Ti:i=1,2,…,N}满足条件(B),则{xn}强收敛于x*∈F(T).     

非扩张映射和广义变分不等式的粘滞逼近法

应用已提出的非扩张映射的粘滞逼近方法,给定初值x_0∈C,考虑一般迭代过程{x_n},g(x_(n+1))=α_nf(x_n)+(1-α_n)SP_C(g(x_n)-λ_nAx_n),n≥0,其中{α_n}■(0,1),S:C→C是非扩张映射,C是实Hilbert空间H的非空闭凸子集.在{α_n}满足合适的条件下可证明,{x_n}强收敛到非扩张映射的不动点集和广义变分不等式解的公共元,且满足某变分不等式.     

Banach空间中渐近非扩张映射的不动点迭代

设D是一致凸Banach空间X的非空闭凸子集 ,T∶D→D是渐近非扩张映射且kn ≥ 1 ,∑ ∞n =1(kn- 1 ) <∞ .设T的不动点集F(T) ≠ ,T是全连续的 (X满足Opial条件 ) ,{xn},{yn},{zn}由定义 2给出 ,如果 ∑∞n =1cn <∞ ,∑ ∞n =1c′n <∞ ,∑ ∞n =1c″n <∞ ,且下列条件之一满足 :(i)b″n ∈ [a ,b] ( 0 ,1 ) ;b′n ∈ [0 ,β];bn ∈[0 ,α],αβ β <1 ;(ii)b′n ∈ [a ,b] ( 0 ,1 ) ;b″n ∈ [a ,1 ];bn ∈ [0 ,b];(iii)bn ∈[a ,b] ( 0 ,1 ) ;b′n ∈ [a ,1 ],则 {xn},{yn},{zn}强收敛于T的不动点 .( {xn}弱收敛于T的不动点 ) .     

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．     

广义复合隐迭代格式逼近非扩张映像公共不动点

提出并使用如下广义复合隐迭代格式逼近非扩张映像族{Ti}Ni=1公共不动点:{xn=αnxn-1 (1-αn)Tnyn,yn=rnxn snxn-1 tnTnxn wnTnxn-1,rn sn tn wn=1,{αn},{rn},{sn},{tn},{wn}∈[0,1],这里Tn=TnmodN.该文提出的广义复合隐迭代格式包含了目前多种迭代格式,因此,所得强弱收敛定理推广及发展了Mann,Ishikawa,XuandOri,等许多作者的结果.     

逼近非扩张非自映像不动点（英文）

设E是一致凸Banach空间,K是E中非空闭凸集且是一个非扩张收缩核,T：K→E是具非空不动点集F（T）：={x∈K：Tx=x}的非扩张映像.设{α_n},{β_n},{γ_n},{α′_n},{β′_n},{γ′_n}是[0,1]中实数列满足α_n＋β_n＋γ_n=α′_n＋γ′_n＋γ′_n=1,对任意初值x_1∈K,定义{x_n}如下（ⅰ）如果对偶空间E＊具有Kadec-Klee性质,那么{x_n}弱收敛于T的某不动点x＊∈F（T）;（ⅱ）若T满足（A）条件,那么{x_n}强收敛于T的某不动点x＊∈F（T）.     

定向集指标非交换鞅的几种收敛性

本文研究了定向集指标非交换鞅的几种收敛性.利用非交换鞅的理论,得到了如下结果:设{xα,Mα}α∈I是一个定向集指标的非交换鞅.则{xα}依L1范数收敛(或弱收敛)的充要条件是{xα}一致可积且满足条件(B):对任意的ε0,存在投影e∈M,使得对任意的y∈M,y≤1及任意的α∈I,有|τ(exαey)|ε.当1p∞时,{xα}依Lp范数收敛(或弱收敛)的充要条件是{xα}在Lp(M)中依Lp范数有界.这也等价于存在一个x∞∈Lp(M),使得xα=Eα(x∞)(α∈I).推广了交换情形中的相应结果.     

Banach空间中一般的强增生算子方程解的迭代逼近

设1＜p≤2,X是实p-一致光滑的Banach空间,TX→X是一强增生算子,研究了用于求方程Tx=f解的带误差的Ishikawa迭代程序分别在条件αn→0(n→∞)与条件0＜α≤αn((A)n≥0)下的强收敛问题,改进与推广了现有的结果.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].