FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

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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。     

锥上减映象的不动点及其在非局部边值问题中的应用

研究锥上一类减映象,得到这类映象不动点的存在性、唯一性和迭代序列的收敛性.其结果在二阶非局部边值问题中得到应用.     

ON POINTWISE R-SUBWEAKLY COMMUTING MAPS AND BEST APPROXIMATIONS

The main purpose of this paper is to prove some common fixed point theorems for pointwise R-subweakly commuting maps on non-starshaped domains in p-normed spaces and locally convex topological vector spaces. As applications, invariant approximation results are established. This work provides extension as well as substantial improvement of several results in the existing literature.     

有限个广义渐近非扩张映射具误差的复合隐迭代过程

在一致凸Banach空间研究了一个新的有限个广义渐近非扩张映射具误差的复合隐迭代过程.利用空间满足Opial条件和算子满足半紧性条件,我们证明了这个隐迭代过程强、弱收敛于有限个广义渐近非扩张映射的公共不动点.这些结果是目前所得成果的完善和推广.     

COUPLED FIXED POINTS OF SKEW INCREASING OPERATORS AND APPLICATIONS

1Intr0ducti0nIllthisPaPerwestudythefordpointsandcouPledfiXedpointsofskewincreasing0PeratorsandtheiraPplicaion.LetXbeaBanachsPaCcwithapartialorderingintr0ducedbythcc0neK-LctF:X-Xbean0peraorinX.FiscaJledinCreasingifF2SFgf0raJl2Sy.Asiswellkllown,inthetheorerns0fhapointforincreasingoPerbo,thereisaninterestinginterreboi0nbetweenPr0pertiesofKandF,thatisThoorem1l1I'I2ILetXbeaBanachpee,partiaJlyorderedbythecolleKGX.Let[a,b]beanordeintervalandF:[a,b]- [a,b]increasin.ThenFhasabop0intif0…     

A Weak Convergence Theorem for A Finite Family of Asymptotically Nonexpansive Mappings

The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.     

渐近非扩张映射不动点的存在与迭代收敛性

主要讨论一致凸Banach空间E中的非空闭凸子集上渐近非扩张映象不动点集非空的充要条件以及修正的Ishikawa迭代序列{xn}收敛到不动点的充要条件,推广与发展了Zeng Luchuan(2001),曾六川(2003),Liu Qihou(2001)等人的相应结果.     

Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings

Let K be a nonempty closed convex and bounded subset of a real Banach space E and T:K→K be uniformly L-Lipschitzian, uniformly asymptotically regular with sequence {ε_n}, and asymptotically pseudocontractive with constant {k_n}, where {k_n} and {ε_n} satisfy certain mild conditions. Let a sequence {x_n} be generated from x₁∈K by x_n+1:=(1−λ_n)x_n+λ_nTⁿx_n−λ_nθ_n(x_n−x₁), for all integers n?1, where {λ_n} and {θ_n} are real sequences satisfying appropriate conditions, then ‖x_n−Tx_n‖→0 as n→∞. Moreover, if E is reflexive, and has uniform normal structure with coefficient N(E) and L<N(E)^1/2 and has a uniformly Gâteaux differentiable norm, and T satisfies an additional mild condition, then {x_n} also converges strongly to a fixed point of T.     

Banach空间中渐近非扩张映射不动点的粘性逼近

在一致凸并具有一致G可微范数的Banach空间中,研究一类渐近非扩张映象迭代序列的收敛性,给出强收敛定理.     

渐近非扩展映象的具误差的Ishikawa迭代序列的新强收敛定理

使用新的证明方法，在去掉数列{an}单调递减的条件下，建立了一致凸Banach空间中的渐近非扩展映象不动点的具误差的Ishikawa迭代序列的新强收敛定理．其结果推广和改进了Schu，Rhoades及周海云等作者的相关结果．     

关于渐近非扩张映象不动点迭代的一点注记

设E是一致凸Banach空间,C是E的非空闭凸子集,T:C→C是具有不动点的渐近非扩张映象．该文证明了在某些适当的条件下,由下列修改了的Ishikawa迭代程序所定义的序列{xn}=xn 1=rpn,pn=(1-an)xn anTmn ryn un,yn=(1-bn)xn bnTkn xn vn, (n≥1)弱收敛到t的不动点．     

Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings

In this work we prove a new strong convergence result of the regularized successive approximation method given by yn＋1 = qnz0 ＋ （1 - qn）T^nyn, n = 1, 2,…,where lim n→∞ qn = 0 and ∞∑n=1 qn=∞ for T a total asymptotically nonexpansive mapping, i.e., T is such that
││T^n x - T^n y││ ≤ x - y ││ ＋ kn^（1）φ（││x - y││） ＋ kn^（2）,where kn^1 and kn^2 are real null convergent sequences and φ：R^＋→R^＋ is continuous such that φ（0）=0 and limt→∞φ（t）/t≤ C for a certain constant C 〉 0.
Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings.     

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...     

Weak Convergence Theorems for Mixed Type Asymptotically Nonexpansive Mappings

The purpose of this paper is to prove some weak convergence theorems for mixed type asymptotically nonexpansive mappings with mean errors in uniformly convex Banach spaces. The results presented in this paper extend the corresponding results in the references.     

逼近一致凸Banach空间中渐近非扩张映象的不动点

借助于B ruck′s不等式,研究了一致凸Banach空间中渐近非扩张映象不动点的具误差的Ish ikaw a迭代序列的强收敛定理.所得的结果推广和改进了Schu,Rhoades,周海云,王绍荣等作者的相应结果.     

On Common Fixed Points of Asymptotically Nonexpansive Mappings in the Intermediate Sense

Some strong convergence theorems of common fixed points of asymptotically nonexpansive mappings in the intermediate sense are obtained. The results presented in this paper improve and extend the corresponding results in Huang, Khan and Takahashi, Chang, Schu, and Rhoades.     

增生算子粘性逼近的强收敛定理

假设$E$为实Banach空间, $A$为具有零点的增生算子. 定义序列 $\{x_n\}$如下: $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n)J_{r_n}x_n$, 这里$\{\alpha_n\}$, $\{r_n\}$ 满足一定条件的序列, 令$J_r=(I+rA)^{-1}$, $r>1$. 假如空间$E$有弱连续对偶映像,或者$E$为一致光滑的,均得到了序列 $\{x_n\}$的强收敛性结果.     

一致正规结构与Reich的公开问题的解答

在具有一致正规结构且其范数是一致Gateaux可微的Banach空间中,研究了Reich提出的公开问题.在给渐近非扩张映象作更适当的假设下,对Reich的公开问题给出了一个肯定的答复.所得结果在下列方面推广与改进了张石生教授的最新结果:(ⅰ)去掉了张教授的较强条件“迭代参数列收敛到零”;(ⅱ)去掉了张教授的较强假设“渐近非扩张映象有不动点”;(ⅲ)也去掉了张教授的较强条件“Banach压缩映象原理生成的序列强收敛”.而且,这些结果也推广与改进了先前由Reich,Shioji,Takahashi,Ueda及Wittmann等多位作者得到的相应结果.     

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