共查询到17条相似文献,搜索用时 78 毫秒
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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. 相似文献
││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. 相似文献
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本文在一致凸的Banach空间中研究一致L-Lipshitzian渐近半伪压缩映射的带平均误差的三步迭代序列.应用新的方法,得到一致L-Lipshitzian渐近半伪压缩映射的一些强收敛的充分必要条件,改进和推广了文[4]中相应的结果. 相似文献
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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. 相似文献
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目的是把对单个渐近T为压缩映射的迭代结果推广到有限个渐近T为压缩映射上.为此,利用数学归纳法的思想,在一定条件下,得出了有限个渐近T为压缩映射强收敛于其公共不动点的结论.此结论推广了以前的结果. 相似文献
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研究了Banach空间中两个不同渐近demi-压缩映射的Ishikawa迭代过程,给出了此Ishikawa迭代序列收敛的充要条件.推广了以前的结论. 相似文献
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Iterative sequences with mixed errors for asymptotically quasi-nonexpansive type mappings in Banach spaces 总被引:1,自引:0,他引:1
The purpose of this paper is to study necessary and sufficient conditions for the Ishikawa iterative sequence with mixed errors
of asymptotically quasi-nonexpansive type mappings in Banach spaces to converge to a fixed point in Banach spaces. The results
presented in this paper complememt, improve and prefect the corresponding results of [1]–[4] and [7]–[9].
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题 总被引:1,自引:0,他引:1
研究了Banach空间中渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题,改进和发展了张石生教授等人的相应结果. 相似文献
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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
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在Banach空间中引入渐近非扩张映象和非扩张映象某些类型的具误差的迭代序列,并研究了这些迭代序列的收敛性问题.本文的结果改进、推广和完善了最新的一些结果. 相似文献
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Ljubomir B. Ćirić 《Czechoslovak Mathematical Journal》1999,49(4):891-899
In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.27. march 80 相似文献
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Banach空间中Ishikawa迭代序列的稳定性和收敛性问题 总被引:1,自引:0,他引:1
在Banach空间的框架下,讨论了中间意义下的渐进非扩张的渐进伪压缩的具平均误差的修正的Ishikawa和Mann迭代序列的收敛性和稳定性之间的等价性问题,改进和推广了以前的结果. 相似文献