均衡问题和不动点问题的粘滞近似方法及其应用

用粘滞近似方法产生了一个新的迭代序列,并证明了该迭代序列强收敛于一个非扩张映射的不动点,同时该不动点也是一个变分不等式和一个均衡问题的共同解.作为应用,另外证明了一个关于非扩张映射和严格伪压缩映射的定理.     

严格伪压缩映像族隐格式迭代逼近不动点几何结果

对非线性算子迭代序列逼近不动点过程的几何结构进行研究,在提出并证明了一个H ilbert空间中收敛序列的钝角原理基础上,应用这个钝角原理研究了严格伪压缩映像族的隐格式迭代序列逼近公共不动点的几何结构.并证明了相应的钝角原理.这个钝角原理表述了严格伪压缩映像族的隐格式迭代序列逼近公共不动点时与公共不动点集形成了钝角关系.这个钝角关系是使用相应内积序列的上极限表示的.事实上这个钝角结果的表述形式也是一个几何变分不等式,迭代序列的极限点即是这个几何变分不等式的解.一方面这个钝角结果表述了严格伪压缩映像族公共不动点隐格式逼近的几何过程,另一方面,这个钝角结果自然是隐格式迭代序列逼近严格伪压缩映像族公共不动点的必要条件.     

Banach空间中关于变分不等式组与严格伪压缩映射的粘滞逼近法

本文利用粘滞逼近法建立了一迭代序列来逼近两个集合的公共元素,这两个集合分别是Banach空间中广义变分不等式组的解集与Banach空间中有限个严格伪压缩映射的公共不动点集.本文证明了该迭代序列强收敛到这两个集合的某一公共元素,且该元素为某一变分不等式的解.本文的结果提高与推广了许多相关结论.     

连续伪压缩映射的黏滞迭代逼近方法

设K是实自反Banach空间E的一个闭凸子集,T：K→K是一个连续伪压缩映射,f：K→K是一个固定的L-Lipschitzian强伪压缩映射．对于任意的t∈(0,1),设x_t是tf+(1-t)T的唯一不动点．我们证明了如果T有不动点且有从E到E~*弱序列连续对偶映像,则当t趋于0时,{x_t}收敛于T的一个不动点．这个结果改进和推广了文[4]的相应结果．     

严格渐进伪压缩映象之修正型Mann迭代算法的强收敛性

本文利用CQ方法获得了k-严格渐进伪压缩映象修正型迭代算法的强收敛结果.此结果推广并改进了T.H.Kim和徐洪坤2006年获得的相应的一主要结果.即,从渐进非扩张映象推广到k-严格渐进伪压缩映象,并且去掉了闭凸子集C的有界性假设条件.     

不动点集和零点集公共元的强弱收敛性

在Hilbert空间中,为了找到渐近严格伪压缩映射的不动点集,极大单调算子与逆强单调映射和的零点集的公共元,文中引进两种迭代格式,在某些条件下得到迭代序列的强弱收敛定理.     

有限簇伪压缩映象和单调映象广义迭代法的强收敛性

在Hilbert空间中,建立了一个关于有限簇伪压缩映象和单调映象的广义迭代方法,并在更弱的条件下证明了该方法所产生的序列强收敛到连续伪压缩映象不动点集和变分不等式解集的某个公共元.     

自反Banach空间中非扩张非自映射的粘滞迭代逼近方法

主要在自反和严格凸的且具有一致G(a)teaux可微范数的Banach空间中研究了非扩张非自映射的粘滞迭代逼近过程,证明了此映射的隐格式与显格式粘滞迭代序列均强收敛到它的某个不动点.     

用Ishikawa迭代程序逼近严格伪压缩映射的不动点

本文证明了定义在Banach空间X中闭凸子集K上的Lipschitz严格伪压缩 映射T的不动点,可由Ishilkawa迭代程序逼近,并给出了更一般的收敛率的估计,从而 统一和发展了近期的一些有关的结果.     

伪压缩和单调映射迭代法的强收敛定理(英文)

本文在Hilbert空间中研究有限个伪压缩映射,严格伪压缩映射和单调映射产生的变分不等式的迭代算法,获得伪压缩映射不动点集和变分不等式解的公共元素的强收敛定理,扩展了许多作者的相关研究.     

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.     

AN ITERATIVE PROCESS FOR FINDING APPROXIMATE SOLUTIONS TO NONLINEAR EQUATIONS OF STRONGLY ACCRETIVE OPERATORS

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.     

Regularized and inertial algorithms for common fixed points of nonlinear operators

This paper deals with a general fixed point iteration for computing a point in some nonempty closed and convex solution set included in the common fixed point set of a sequence of mappings on a real Hilbert space. The proposed method combines two strategies: viscosity approximations (regularization) and inertial type extrapolation. The first strategy is known to ensure the strong convergence of some successive approximation methods, while the second one is intended to speed up the convergence process. Under classical conditions on the operators and the parameters, we prove that the sequence of iterates generated by our scheme converges strongly to the element of minimal norm in the solution set. This algorithm works, for instance, for approximating common fixed points of infinite families of demicontractive mappings, including the classes of quasi-nonexpansive operators and strictly pseudocontractive ones.     

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Lipschitz伪压缩映射黏滞迭代逼近方法的强收敛

K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*.     

Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces

In this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth Banach spaces. First, we prove that the S-iteration process recently introduced by Sahu in [14] converges strongly to a unique fixed point of a mapping T, where T is κ-strongly pseudocontractive mapping from a nonempty, closed and convex subset C of a smooth Banach space into itself. It is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of λ_i-strictly pseudocontractive mappings from C into itself. Our results extend and improve some very recent theorems in fixed point theory and variational inequality problems. Particularly, the results presented here extend some theorems of Reich (1980) [1] and Yamada (2001) [15] to a general class of λ-strictly pseudocontractive mappings in uniformly smooth Banach spaces.     

逼近严格伪压缩映象不动点的Ishikawa迭代程序

Let(X,‖·‖ ) be a Banach space.Let K be a nonempty closed,convex subset of Xand T∶K→K.Assume that T is Lipschitzian,i.e.there exists L>0 such that‖ T(x) -T(y)‖≤ L‖ x -y‖for all x,y∈K.Withoutloss of generality,assume that L≥ 1 .Assume also that T is strictly pseudocontractive.According to[1 ] this may be statedas:there exists k∈ (0 ,1 ) such that‖ x -y‖≤‖ x -y + r[(I -T -k I) x -(I -T -k I) y]‖for all r>0 and all x,y∈ K.Throughout,let N denote the set of positive in…     

严格伪压缩映象的Ishikawa 迭代序列的收敛率估计

It is shown that any fixed point of each l.ipschitzian, strictly pseudocontractive mapping 7“ on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure. The argument in this paper provides a convergence rate estimate.Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results.     

关于Ishikawa迭代程序逼近严格伪压缩映象的不动点问题

设X是一Banach空间，K是X的闭凸子集，T：K→K是严格伪压缩的Lipschitz映象。我们证明了T的任何不动点可用Ishikawa迭代程序来范数逼近，并提供了收敛率的估计。本文结果在一定程序上推广与概括了Sastry与Babu[2]的定理1，在一定程度上改进与推广了Liu[1]的定理1与定理2。