Banach空间中渐近正则半群的不动点定理

设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t)t∈S}都有不动点.进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.     

Banach空间中渐近正则的Lipschitz半群的不动点定理

本文首先定义了渐近正则的Ｌｉｐｓｃｈｉｔｚ半群的概念．其次，证明了ｐ一致凸Ｂａｎａｃｈ空间中渐近正则的Ｌｉｐｓｃｈｉｔｚ半群的不动点定理．同时也证明了具有正规结构系数的一致凸Ｅａｎａｃｈ空间中的渐近正则的Ｌｉｐｓｃｈｉｔｚ半群的一个新的不动点定理．     

关于Banach空间中渐近非扩张型半群的不动点的存在性

设C是具有弱一致正规结构的Banach空间X的非空弱紧凸子集, T={T(t):t∈S}是渐近非扩张型半群, 且每个T(t)在C上连续. 该文证明了如下结论:(i) 若X是一致凸的, 则F(T) 非空;(ii) 若T={T(t):t∈S}满足lim inf_{t→∞,t in S}|‖T(t)‖|<+∞, 且在C上弱渐近正则, 则F(T)非空, 其中|‖T(t)‖|是T(t)的精确的Lipsch itz常数,F(T)是T(t),t∈S的所有公共不动点之集.     

一般Banach空间中渐近非扩张型半群的不动点定理

该文首先在一般Banach空间中对渐近非扩张型半群证明了两个不动点存在定理,并由此给出了渐近非扩张型半群Mann型迭代序列的强收敛定理.该文的主要结果将Suzuki和Takahashi的相应结果推广到non-Lipschitzian半群情形.     

关于Banach空间中渐近非扩张型半群的不动点与渐近行为

Let X be a Banach space with a weakly continuous duality map Jφ,C a non-empty weakly compact convex subset of X, and T:(T(t):t∈S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K∩F(T)≠0 is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit {u(t):t∈S} of T converges weakly to a point in F(T) if and only if {u(t):t∈S}is weakly asymptotically regular.     

一般Banach空间中非Lipschitzian可逆半群的不动点定理

首先在一般Banach空间中对渐近非扩张型左可逆半群给出了两个不动点存在性定理.同时利用这些结果,得到了渐近非扩张型左可逆半群迭代序列的强收敛定理.主要结果将一些已知结果推广至非Lipschitzian左可逆半群的情形,而且即使在交换半群情形它们也是新的.     

Banach空间中非Lipschitz映象的连续半群的不动点定理

设E是一实的p一致凸Banach空间.利用渐近中心,E中范数不等式和逐次逼近的思想,本文证明了E中非Lipschitz映象的连续半群的不动点存在的定理.该定理本质上把Lipschitz半群的不动点存在性的研究推广到了非Lipschitz映象的连续半群的情况.另一方面,应用该定理,还得到了非Lipschitz映象的渐近非扩张型半群的渐近行为方面的一些结果.     

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.     

Banach空间中渐近非扩张型半群的遍历定理

对带Opial条件的Banach空间中非扩张半群的不动点理论进行推广,得到了带Opial条件的Banach空间中渐近非扩张型半群的遍历收敛定理.     

关于Banach空间非扩张半群的强收敛定理

在Banach空间框架下,建立了几个关于非扩张半群显式迭代序列的强收敛定理．所得结果不仅推广和改进了Shioji-Takahashi,Suzuki,Xu以及Aleyner-Reich等人的相应结果,而且还部分肯定地回答了Suzuki和Xu提出的两个公开问题．     

Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups

Let X be a Banach space with a weak uniform normal structure and C a non–empty convexweakly compact subset of X. Under some suitable restriction, we prove that every asymptoticallyregular semigroup T = {T(t) : t ∈¸ S} of selfmappings on C satisfying

${\mathop {\lim \inf }\limits_{S \mathrel\backepsilon t \to \infty } }{\left| {{\left\| {T(t)} \right\|}} \right|} < {\text{WCS}}(X)$

has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and\({\left| {{\left\| {T(t)} \right\|}} \right|}\) is the exact Lipschitz constant of T(t).     

一致光滑Banach空间中渐近伪压缩映象不动点的迭代逼近

本文研究用于逼近一致光滑Banach空间中渐近伪压缩映象不动点的具误差的修改了的Ishikawa 型与Mann型迭代程序的收敛性,改进和发展了文[1]的相应结果及他人的结果.     

ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES

61. Introduction and PreliminariesLet C be a nonempty subset Of a Banal spare X. Then a mapping T: C -- C is saidto be a LiPSdrizian maPPing if, for ear integer n 2 1, there eallts a constant km > 0' such that Ilaal ~ chill S k.llx ~ all for all ale E C. A Lipschitzian mapping T is saidto be ~ k-LiPSdszian if km = k for all n 2 1, nonerpansive if km = 1 for alln 2 1, eleCtively. Moreover, a maPPing T: C - C is called asymptotically regularll'191if Asllgu 'z ~ chill = 0 for all 2 E…     

Banach空间中渐近非扩张映象不动点的迭代逼近问题

本文研究Banach空间中渐近非扩张映象和渐近伪压缩映象不动点的迭代逼近问题,本文结果是[4,5,7]中相应结果的发展和改进。     

Banach空间中渐近非扩张型映象的Ishikawa迭代序列的收敛问题

文章研究了Banach空间中渐近非扩张型映象的具误差的修正Ishikawa迭代序列的收敛问题，所得结果改进和发展了文献[1-6]的相关结果。     

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   

COMMON FIXED POINT THEOREMS FOR THREE MAPS IN DISCONTINUOUS Gb-METRIC SPACES

In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or Gb-metric. In this paper, we prove a common fixed point theorem for three mappings in Gb-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result.     

FIXED POINT THEOREMS FOR MULTI-VALUED MAPPINGS IN LOCALLY CONVEX SPACES

<正> Throughout the present paper it is assumed that E is a real,locally convex,Hausdorfftopological vector space,and X(?)E a nonempty compact convex subset.A multi-valuedmapping F:X→2~E is said to be upper(lower) semicontinuous if for any open(closed) setU(?)E the set{x∈X|F(x)(?)U)is open (closed) in X;or,equivalently,for any closed(open) set V(?)E the set{X∈X|F(x)∩ V(?)(?)}is closed (open) in X.Moreover,F