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 ) .     

Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理

研究了Lipschitz伪压缩映射的黏滞迭代方法.设E为一致光滑Bannach空间,K为E的闭凸子集,TK→K为Lipschitz伪压缩映射且其不动点集F(T)非空,f为K上的压缩映射且t∈(0,1).若黏滞迭代路径{xt},xt=(1-t)f(xt) tTxt且对任意初始向量x1∈K,迭代序列{xn}定义为xn 1=λnθnf(xn) [1-λn(1 θn)]xn λnTxn,则当t→1-和n→∞时,{xt}和{xn}都强收敛于T的不动点,同时该不动点还是一类变分不等式的解.     

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.     

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．     

序列覆盖的闭映射保持可度量性

设f:X→Y是连续的满映射. f称为序列覆盖映射,若{y})是Y中的收敛序列,则存在X中的收敛序列{xn},使得每一xn∈f-1(yn);f称为1序列覆盖映射,若对于每-y∈Y,存在x∈f-1(y),使得如果{yn}是Y中收敛于点y的序列,则有X中收敛于点x的序列{xn},使得每一xn∈f-1(yn).本文研究度量空间序列覆盖的闭映射之构造,否定地回答了Topology and its Applications上提出的一个问题.     

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.     

Banach空间中渐近非扩张映象的带误差的修正的Ishikawa与Mann迭代程序

设E是满足Opial条件的一致凸Banach空间,C是E的一非空闭凸子集,T:C→C是渐近非扩张映象.又设对任给的x1∈C,序列{xn}由下列带误差的修正的Ishikawa迭代程序生成:其中, 是C中的序列,使得 且数列 满足下列条件(i)和(ii)之一: (i)tn∈[a,b]且sn∈[O,b];(ii)tn∈[a,b]且sn∈[a,b],这里,常数a,b满足0相似文献   

具误差隐格式迭代逼近严格伪压缩映像族公共不动点

设K是实Banach空间E中非空闭凸集, {Ti}i=1N是N个具公共不动点集F的严格伪压缩映像, {an}(?)[0,1]是实数列, {un}(?)K是序列,且满足下面条件设X0∈K,{xn}由下式定义xn=αnxn-1 (1-αn)Tnxn-un-1,n≥1其中Tn=TnmodN,则有下面结论(i)limn→∞‖xn-p‖存在,对所有P∈F; (ii)limn→∞d(xn,F)存在,当d(xn,F)=infp∈F‖xn-p‖; (iii)liminfn→∞‖xn-Tnxn‖=0．文中另一个结果是,如果{xn}(?){1-2-n,1},则{xn}收敛．文中结果改进与扩展了Osilike(2004)最近的结果,证明方法也不同．     

CWC映射和度量化定理

利用CWC映射,本文获得了对称度量空间和g可度量空间的特征,建立了几个度量化定理,改进了一些已知结果．主要的定理是证明正则空间X是可度量化空间当且仅当存在X上的CWC映射g满足如下条件: (Ⅰ)若序列{xn}和{yn}对于每一n∈N有xn∈g(n,yn)且xn→x,则yn→x．(Ⅱ)若序列{xn}和{yn}对于每一n∈N有yn∈g(n,yn)且xn→x,则yn→x．     

Banach空间中渐近伪压缩映射的黏滞近似不动点序列

首先给出了渐近伪压缩映射的黏滞近似不动点序列的新定义,继而证明了如下逼近定理:令K为实Banach空间E的非空闭凸有界子集,T:K→K为一致L-Lipschitz、具数列{εn}的一致渐近正则、具数列{kn}的渐近伪压缩映射.假设迭代序列{xn}定义为:x1∈K,对n≥1,xn+1:=λnθnf(xn)+[1-λn(1+θn)]xn+λnTnxn,其中{λn},{θn}(0,1)且满足一定条件,则:当n→∞时,‖xn-Txn‖→0.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.