共查询到17条相似文献,搜索用时 125 毫秒
1.
设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设K是实Banach空间E中非空闭凸集,{Ti}i=1^N是N个具公共不动点集F的严格伪压缩映像,{αn}包括于[0,1]是实数例,{un}包括于K是序列,且满足下面条件(i)0〈α≤αn≤1;(ii)∑n=1∞(1-αn)=+∞.(iii)∑n=1∞ ‖un‖〈+∞.设x0∈K,{xn}由正式定义xn=αnxn-1+(1-αn)Tnxn+un-1,n≥1,其中Tn=Tnmodn,则下面结论(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)lim infn→∞‖xn-Tnxn‖=0.文中另一个结果是,如果{xn}包括于[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。 相似文献
2.
设$K$是自反的并且具有一致Gateaux可微范数的Banach空间$E$的非空有界闭凸子集.设$T:K\rightarrow K$是一致连续的伪压缩映象.假设$K$的每一非空有界闭凸子集对非扩张映象具有不动点性质.设$\{\lambda_n\}$是$(0,\frac{1}{2}]$中序列满足: (i) $\lim_{n\rightarrow \infty}\lambda_n=0$; (ii) $\sum_{n=0}^{\infty}\lambda_n=\infty$.任给$x_1\in K$,定义迭代序列$\{x_n\}$为:$x_{n+1}=(1-\lambda_n)x_n+\lambda_nTx_n-\lambda_n(x_n-x_1),n\geq 1.$若$\lim_{n\rightarrow \infty}\|x_n-Tx_n\|=0$, 则上述迭代产生的$\{x_n\}$强收敛到$T$的不动点. 相似文献
3.
设$E$为一致光滑Banach空间,$A:E\to E$为有界次连续广义${\it \Phi} $-增生算子满足:对任意$x_0\in E$,选取$m\ge 1$,使得$\| x_0 - x^* \| \le m$且$\mathop {\underline {\lim } }\limits_{r \to \infty } {\it \Phi} (r) > m\left\| {Ax_0 } \right\|$.设$\{C_n\}$为$[0,1]$中数列满足控制条件: i)$C_n\to 0\,(n\to\infty)$; ii)$\sum\limits_{n = 0}^\infty {C_n } = \infty $.设$\{x_n\}_{n\ge0}$由下式产生x_{n + 1} = x_n - C_n Ax_n ,\q n \ge 0, \eqno{(@)}$$则存在常数$a>0$,当$C_n < a$时,$\{x_n\}$强收敛于$A$的唯一零点$x^{*}$. 相似文献
4.
崔欢欢 《数学物理学报(A辑)》2014,34(3):755-759
主要研究求解增生算子零点问题的一类算法:x_(n+1)=α_nu+(1-α_n)((1-λ)x_n+λJ_r_nx_n),其u是固定向量,λ∈(0,1),{r_n}和{α_n}是实数列,J_r_n表示增生算子A的预解式.其中(r_n)收敛是保证算法收敛的一个充分条件,该文主要证明了此条件可减弱为limn|1-(r_n+1)/r_n|=0. 相似文献
5.
阶为$n$的图$G$的圈长分布是序列$(c_1,c_2,\cdots,c_n)$, 其中$c_i$ 是图$G$ 中长为$i$的圈数.设$A\subseteq E(K_{n,r})$.本文得到如下结果: 若$\mid A\mid =2$,且$n\leq r\leq \min\{n+6,2n-5\}$,则$G=K_{n,r}-A$是由它的圈长分布确定的;若$\mid A\mid =3$,且$n \leq r\leq \min\{n+6,2n-7\}$,则$G=K_{n,r}-A$也是由它的圈长分布确定的. 相似文献
6.
图$G$的$(\mathcal{O}_{k_1}, \mathcal{O}_{k_2})$-划分是将$V(G)$划分成两个非空子集$V_{1}$和$V_{2}$, 使得$G[V_{1}]$和$G[V_{2}]$分别是分支的阶数至多$k_1$和$k_2$的图.在本文中,我们考虑了有围长限制的平面图的点集划分问题,使得每个部分导出一个具有有界大小分支的图.我们证明了每一个围长至少为6并且$i$-圈不与$j$-圈相交的平面图允许$(\mathcal{O}_{2}$, $\mathcal{O}_{3})$-划分,其中$i\in\{6,7,8\}$和$j\in\{6,7,8,9\}$. 相似文献
7.
李云霞 《数学物理学报(A辑)》2006,26(5):675-687
该文主要讨论的是滑线性过程 $X_k=\sum\limits_{i=-\infty}^\infty a_{i+k}\varepsilon_i$,其中 $\{\varepsilon_i; -\infty$\varphi$ -混合或负相伴随机变量序列,$\{a_i;-\inftyp$, 若 $E|\varepsilon_1|^r<\infty$$\lim_{\epsilon\searrow 0}\epsilon^{2(r-p)/(2-p)}\sum\limits_{n=1}^\infty n^{r/p-2}P\{|S_n|\geq \epsilonn^{1/p}\}=\frac{p}{r-p}E|Z|^{2(r-p)/(2-p)},$ 其中 $Z$ 是服从均值为零,方差为 $\tau^2=\sigma^2\cdot(\sum\limits_{i=-\infty}^\infty a_i)^2$的正态分布. 相似文献
8.
设$n+1$个$m\times n(m\geq n)$实矩阵$\{A_i\}_{i=0}^n$和给定的$n$个正数$\{\sigma_i^{*}\}_{i=1}^n$.本文研究如下的逆奇异值问题:求$n$个实数$\{c_i^{*}\}_{i=1}^n$,使得矩阵$A_0+c_1^{*}A_1+\cdots +c_n^{*}A_n$有奇异值$\{\sigma_i^*\}_{i=1}^n.$基于矩阵方程,我们给出了求解逆奇异值问题的一个新的算法,并证明了它的二阶收敛特性.该算法可以看成是Aishima[Linear Algebra and its Applications,2018,542:310-333]中逆对称特征值问题算法的推广.数值例子表明算法的有效性. 相似文献
9.
陆传荣 《数学物理学报(A辑)》2006,26(3):361-364
设$\{\xi_n, n\geq 1\}$是正的随机变量序列, $\ep \xi_1=\theta>0$, 设$S_n = \sum\limits_{i=1}^n \xi_i, Y_n=n\theta\log (S_n/(n\theta))$. 在该文中, 当$\{\xi_n\}$是独立同分布或强平稳$\varphi$ -混合的正随机变量序列时,作者给出功率和$\{Y_n\}$用Wiener过程的强逼近结果. 相似文献
10.
1. Let X be the conjugate of a separable Banach space satifying the *-Opial
condition, i. e., if \[\{ {x_n}\} \subset x,{x_n}\mathop \to \limits^{{w^*}} {x_\infty },{x_\infty } \ne y\], then\[\mathop {\overline {\lim } }\limits_{n \to \infty } ||{x_n} - {x_\infty }|| < \mathop {\overline {\lim } }\limits_{n \to \infty } ||{x_n} - y||\]
for rxample \[X = {l_1}\]
Let K be a nonempty weak* closed convex subset of X.
The main results are:
Theorem 1. Suppose T is a ooniinuons mappings of K into itself such that for
every \[x,y \in K\],\[||Tx - Ty|| \le a||x - y|| + b\{ ||x - Tx|| + ||y - Ty||\} + c\{ ||x - Ty|| + ||y - Tx||\} \]
where real numbers \[a,b,c \ge 0\] and \[a + 2b + 2c = 1\]. Suppose also K is bounded.Then T has at least one fixed point in K.
Theorem 2. Let T be a mapping of K into itself, and \[a(x,y),b(x,y),c(x,y)\]be real functions such that for all\[x,y \in K\]
\[||Tx - Ty|| \le a(x,y)||x - y|| + b(x,y)\{ ||x - Tx|| + ||y - Ty||\} + c(x,y)\{ ||x - Ty|| + ||y - Tx||\} \]
and \[a(x{\rm{y}},y){\rm{ + }}2b(x,y){\rm{ + }}2c(x,y) \le 1\]
Suppose there exists \[x \in K\] such that \[O(x) = \{ {T^n}x\} _{n = 1}^\infty \] is bounded and
\[\mathop {\inf }\limits_{y,z \in o(x)} c(y,z) > 0\]
Then T has at least one fixed point z in K and \[{T^n}x\mathop \to \limits^{{w^*}} z\].
2. We denote \[CL(x) = \{ A;nonempty{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} closed{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} subset{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} of{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} X\} \]
\[K(x) = A;nonempty{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} closed{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} subset{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} of{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} x\} \]
here X is a complete metric space with metric d.
On \[CL(x)\] and \[K(x)\] we introduce the generalized Hausdorff distance \[H(,)\],
The main results are:
Theorem 3. Suppose \[\{ T,S\} \] is a pair of set-valued mappings of X into \[CL(x)\],which satisfies the following condition:
\[H(Tx,Sy) \le hMax\{ d(x,y),D(x,Tx),D(y,Sy),\frac{1}{2}[D(x,Sy) + D(y,Tx)]\} \]
for each \[x,y \in K\], where 0相似文献
11.
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. 相似文献
12.
Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti : K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^(i)n} and asymptotically pseudocontractive mappings with sequences {κ^(i)n}, where {κ^(i)n} and {ε^(i)n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn:= (1-μn)xn+μnT^nnxn, xn+1 := λnθnx1+ [1 - λn(1 + θn)]xn + λnT^nnzn for all integer n ≥ 1, where Tn = Tn(mod N), and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ||xn- Tixn||→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu. 相似文献
13.
14.
Banach空间中伪压缩映象不动点的迭代逼近 总被引:1,自引:0,他引:1
Let K be a nonempty closed convex subset of a real p-uniformly convex Banach space E and T be a Lipschitz pseudocontractive self-mapping of K with F(T) := {x ∈ K:Tx=x}≠φ. Let a sequence {xn} be generated from x1 ∈ K by xn+1 = anxn,+ bnTyn++ cnun, yn= a′nxn~ + b′nTx,+ c′n,un, for all integers n ≥ 1. Then ‖xn - Txn,‖ → 0 as n→∞. Moreover, if T is completely continuous, then {xn} converges strongly to a fixed point of T. 相似文献
15.
涉及无限族非扩张映象$\{T_n\}_{n=1}^\infty$的迭代算法$x_{n 1}=\alpha_{n 1}f(x_n) (1-\alpha_{n 1})T_{n 1}x_n$ 总被引:1,自引:0,他引:1
Under the framework of uniformly smooth Banach spaces, Chang proved in 2006 that the sequence {xn} generated by the iteration xn+1 =αn+1f(xn) + (1 - αn+1)Tn+1xn converges strongly to a common fixed point of a finite family of nonexpansive maps {Tn}, where f : C → C is a contraction. However, in this paper, the author considers the iteration in more general case that {Tn} is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping. 相似文献
16.
Lin Zhengyan 《数学年刊B辑(英文版)》1998,19(3):281-292
§1.IntroductionandResultsLet{Xn,n1}beasequenceofrandomvariableswithacommondistributionfunctionF(x)andletXn1Xn2…Xnnbetheor... 相似文献
17.
Let E be a real reflexive strictly convex Banach space which has uniformly Gâteaux differentiable norm. Let ${\mathcal{S} = \{T(s): 0 \leq s < \infty\}}$ be a nonexpansive semigroup on E such that ${Fix(\mathcal{S}) := \cap_{t\geq 0}Fix( T(t) ) \not= \emptyset}$ , and f is a contraction on E with coefficient 0 < α < 1. Let F be δ-strongly accretive and λ-strictly pseudo-contractive with δ + λ > 1 and ${0 < \gamma < \min\left\{\frac{\delta}{\alpha}, \frac{1-\sqrt{ \frac{1-\delta}{\lambda} }}{\alpha} \right\} }$ . When the sequences of real numbers {α n } and {t n } satisfy some appropriate conditions, the three iterative processes given as follows : $${\left.\begin{array}{ll}{x_{n+1} = \alpha_n \gamma f(x_n) + (I - \alpha_n F)T(t_n)x_n,\quad n\geq 0,}\\ {y_{n+1} = \alpha_n \gamma f(T(t_n)y_n) + (I - \alpha_n F)T(t_n)y_n,\quad n\geq 0,}\end{array}\right.}$$ and $$ z_{n+1} = T(t_n)( \alpha_n \gamma f(z_n) + (I - \alpha_n F)z_n),\quad n\geq 0 $$ converge strongly to ${\tilde{x}}$ , where ${\tilde{x}}$ is the unique solution in ${Fix(\mathcal{S})}$ of the variational inequality $${ \langle (F - \gamma f)\tilde {x}, j(x - \tilde{x}) \rangle \geq 0,\quad x\in Fix(\mathcal{S}).}$$ Our results extend and improve corresponding ones of Li et al. (Nonlinear Anal 70:3065–3071, 2009) and Chen and He (Appl Math Lett 20:751–757, 2007) and many others. 相似文献