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SOME RESULTS ON GENERALIZED EQUILIBRIUM PROBLEMS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS 被引量:8
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作者 Jong Kyu Kim Sun Young Cho 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期2041-2057,共17页
In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution s... In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings. 展开更多
关键词 equilibrium problem nonexpansive mapping inverse-strongly monotone mapping strictly pseudocontractive mapping
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ISHIKAWA ITERATIVE PROCEDURE FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS 被引量:3
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作者 Zeng LuchuanDept. of Math., Shanghai Normal Univ.,Shanghai 200234. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第3期283-286,共4页
It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper pro... It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence. 展开更多
关键词 fixed point arbitrary Banach space Lipschitzian strictly pseudocontractive mapping Ishikawa iterative procedure
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CONVERGENCE RATE ESTIMATE OF ISHIKAWA ITERATIVE SEQUENCE FOR STRICTLY PSEUDOCONTRACTIVE MAPPINGS 被引量:1
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作者 Zeng LuchuanDept.ofMath.,ShanghaiNormalUniv.,Shanghai200234,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第2期189-192,共4页
Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in th... Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T 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 resultin this paper improves,generalizes and summarizes some important and el- egant recent results 展开更多
关键词 arbitrary Banach space Lipschitzian mapping strictly pseudocontractive mapping fixed POINTS Ishikawa iterative procedure
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CONVERGENCE OF HYBRID VISCOSITY AND STEEPEST-DESCENT METHODS FOR PSEUDOCONTRACTIVE MAPPINGS AND NONLINEAR HAMMERSTEIN EQUATIONS
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作者 Yekini SHEHU Olaniyi.S.IYIOLA 《Acta Mathematica Scientia》 SCIE CSCD 2018年第2期610-626,共17页
In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping (... In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping (assuming existence) and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method. 展开更多
关键词 Lipschitz pseudocontractive mapping monotone operators equations of Hammerstein type strong convergence Hilbert spaces
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Iterative Approximation of Fixed Points for Uniformly Continuous and Strongly Pseudocontractive Mappings in Smooth Banach Spaces
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作者 周海云 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第2期42-46, ,共5页
With an inequality and some analysis techniques,iterative approximation of fixed points for uniformly continuous and strongly pseudocontractive mappings in smooth Banach spaces is studied,and the recent corresponding ... With an inequality and some analysis techniques,iterative approximation of fixed points for uniformly continuous and strongly pseudocontractive mappings in smooth Banach spaces is studied,and the recent corresponding results of Chidume are improved. 展开更多
关键词 Ishikawa iteration process strong pseudocontraction strongly accretive mapping smooth Banach space
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ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS
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作者 曾六川 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2003年第1期66-70,共5页
The purpose of this paper is to investigate the problem of approximatingfixed points of non- Lipschitizian asymptotically pseudocontractive mappings in an ar-bitrary real Banach space by the modified Ishikawa iterativ... The purpose of this paper is to investigate the problem of approximatingfixed points of non- Lipschitizian asymptotically pseudocontractive mappings in an ar-bitrary real Banach space by the modified Ishikawa iterative sequences with errors. 展开更多
关键词 BANACH空间 渐近映射 ISHIKAWA迭代序列 不动点 迭代逼近
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BRUCK FORMULA FOR A PERTURBED LIPSCHITZIAN ITERATION OF LIPSCHITZ PSEUDOCONTRACTIVE MAPS
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作者 Krishna Kumar B. K. Sharma ZHOU Zhe-wei 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第11期1427-1434,共8页
The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution ( fixed point) of pseudocontractive operators and its v... The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution ( fixed point) of pseudocontractive operators and its variants. The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique. This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence. Our results generalize the results of Chidume and Zegeye. 展开更多
关键词 pseudocontractive map perturbed Lipschitzian iteration fixed point uniformaly Gateaux differential norm
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CONVERGENT PROBLEM OF ITERATIVE SEQUENCES FOR NONLINEAR MAPPINGS WITH ERROR MEMBERS IN BANACH SPACES 被引量:5
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作者 SunZhaohong NiYongqin HeChang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期81-89,共9页
In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are inv... In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results. 展开更多
关键词 asymptotically nonexpansive mapping asymptotically pseudocontractive mapping modified Ishikawa iterative sequence with errors arbitrary Banach space fixed point.
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Strong Convergence Theorems for Two Lipschitzian Peseudocontractive Mappings in Banach Spaces
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《大学数学》 2013年第5期28-32,共5页
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An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings 被引量:2
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作者 Liang-gen Hu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第2期281-288,共8页
In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the mod... In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic. 展开更多
关键词 Implicit iteration process with errors uniformly convex strictly asymptotically pseudocontractive mappings common fixed point
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On Characterization of Iterative Approximation for Asymptotically Pseudocontractive Mappings
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作者 曾六川 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2005年第2期279-286,共8页
Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ... Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - (tn)/(Lkn))u + (tn)/(Lkn)Tnx(?)x ∈ C, where {tn}(?)[0,1). Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized. 展开更多
关键词 fixed point asymptotically pseudocontractive mapping uniform Lipschitzian mapping uniform normal structure Banach contraction principle.
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Approximating Fixed Points of Pseudocontractive Mapping in Banach Spaces 被引量:1
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作者 YAO Yong-hong CHEN Ru-dong 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第1期169-176,共8页
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 ... 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. 展开更多
关键词 pseudocontractive mappings p-uniformly convex Banach spaces Ishikawa iterationprocess with errors.
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Iterative Schemes for a Family of Finite Asymptotically Pseudocontractive Mappings in Banach Spaces 被引量:1
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作者 GU Feng 《Journal of Mathematical Research and Exposition》 CSCD 2009年第5期864-870,共7页
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 as... 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. 展开更多
关键词 approximated fixed point sequence uniformly asymptotically regular mapping asymptotically pseudocontractive mapping.
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Strong Convergence Theorems for Strictly Asymptotically Pseudocontractive Mappings in Hilbert Spaces
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作者 Shi Sheng ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第7期1367-1378,共12页
The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a... The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67(7), 2258-2271 (2007)], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 (2006)], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 (2006)], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 (2003)], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329(1), 336-346 (2007)], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 (2007)], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26(11), 1835-1842 (1996)], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12(2), 77-88 (2002)], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 (2007)]. 展开更多
关键词 Strictly asymptotically pseudocontractive mapping strictly pseudocontractive mapping of Browder Petryshyn type CSQ methods common fixed point
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Strong convergence theorem for a generalized equilibrium problem and a k-strict pseudocontraction in Hilbert spaces
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作者 张石生 饶若峰 黄家琳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第6期685-694,共10页
The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontract... The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in the Hilbert space. The presented results extend and improve the corresponding results reported in the lit-erature. 展开更多
关键词 k-strict pseudocontractive mapping equilibrium problem a-inverse-stronglymonotone mapping variational inequality
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A Note on Approximating Fixed Points of Pseudocontractive Mappings
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作者 YAO Yong Hong 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期740-744,共5页
Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T : K →K be a uniformly continuous pseudocontractive mapping. Suppose every close... Let K be a nonempty bounded closed convex subset of a real reflexive Banach space E with a uniformly Gateaux differentiable norm. Let T : K →K be a uniformly continuous pseudocontractive mapping. Suppose every closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Let {λn} C (0,1/2] be a sequence satisfying the conditions: (i) limn→∞λn=0; (ii) ∑n=0^∞ λn=∞. Let the sequence {xn} be generated from arbitrary x1∈K by xn+1 = (1 -λn)xn + λnTxn -λn(xn - x1), n ≥ 1. Suppose limn→∞‖xn - Txn‖ = 0. Then {xn} converges strongly to a fixed point of T. 展开更多
关键词 pseudocontractive mapping fixed point uniformly Gateaux differentiable norm strong convergence.
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Strong Convergence Theorems for Asymptotically Strictly Pseudocontractive Maps in Hilbert Spaces
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作者 QIN Xiao Long WU Chang Qun SHANG Mei Juan 《Journal of Mathematical Research and Exposition》 CSCD 2009年第1期43-51,共9页
The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive ... The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others. 展开更多
关键词 nonexpansive mappings strictly pseudocontractive mappings Hilbert spaces projection.
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非Lipschitz渐近伪压缩映象不动点的迭代逼近 被引量:16
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作者 张树义 宋晓光 +1 位作者 万美玲 李丹 《北华大学学报(自然科学版)》 CAS 2014年第5期581-587,共7页
在去掉{xn}有界的条件下,从而没有使用{Tnxn}和{Tnyn-yn}的有界性条件,在实Banach空间中建立了非一致Lipschitz的渐近伪压缩映象不动点的更一般的具混合误差的修改的Ishikawa迭代序列的强收敛定理,从而改进和推广了已有的相关结果.
关键词 实BANACH空间 渐近伪压缩型映象 渐近非扩张映象 不动点 具混合广义误差的修改的Ishikawa迭代序列
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Hilbert空间中广义平衡问题与k-严格伪压缩映象的强收敛定理 被引量:7
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作者 张石生 饶若峰 黄家琳 《应用数学和力学》 CSCD 北大核心 2009年第6期639-647,共9页
在Hilbert空间中引进并研究了一种新的迭代算法,借以寻求广义平衡问题解集与k-严格伪压缩映象不动点集的一公共元.所得到的结果,推广并改进了最近一些人所发布的新结果.
关键词 k-严格伪压缩映象 平衡问题 a-逆强单调映象 变分不等式
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含m-增生算子或φ-伪压缩映象具误差的Ishikawa迭代的收敛性问题 被引量:15
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作者 颜敏 李素梅 何震 《应用泛函分析学报》 CSCD 2000年第4期359-370,共12页
主要研究了 m-增生算子以及 -伪压缩映象的分别带两种误差的 Ishikawa迭代序列的收敛性问题 .推广了
关键词 M-增生算子 ¢-伪压缩映象 强伪压缩映象 ISHIKAWA迭代 收敛性
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