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ITERATIVE APPROXIMATION OF FIXED POINTS OF (ASYMPTOTICALLY) NONEXPANSIVE MAPPINGS 被引量:8
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作者 Zeng LuchuanDept. of Math.,Shanghai Normal Univ.,Shanghai 200234. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第4期402-408,共7页
Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpans... Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions. 展开更多
关键词 Fixed point (asymptotically)nonexpansive mapping modified Ishikawa iteration process Frechet differentiable norm Opial condition.
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ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS 被引量:1
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作者 曾六川 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期246-254,共9页
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak conver... This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results. 展开更多
关键词 Semitopological semigroup almost asymptotically nonexpansive type mapping almost orbit asymptotic behavior
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A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space
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作者 Hafiz Fukhar-ud-din Amna Kalsoom Safeer H Khan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第3期274-286,共13页
We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results pres... We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results. 展开更多
关键词 uniformly convex hyperbolic space asymptotically nonexpansive mapping common fixed point strong convergence
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APPROXIMATING COMMON FIXED POINTS OF NEARLY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
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作者 Safeer Hussain Khan Mujahid Abbas 《Analysis in Theory and Applications》 2011年第1期76-91,共16页
We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings. We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings ... We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings. We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence. 展开更多
关键词 iteration scheme nearly asymptotically nonexpansive mapping rate of con-vergence common fixedpoint weak and strong convergence
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A Weak Convergence Theorem for A Finite Family of Asymptotically Nonexpansive Mappings
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作者 Kan Xu-zhou Guo Wei-ping 《Communications in Mathematical Research》 CSCD 2014年第4期295-300,共6页
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.
关键词 asymptotically nonexpansive mapping weak convergence common fixed point uniformly convex Banach space
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Strong Convergence Theorems for Mixed Type Asymptotically Nonexpansive Mappings
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作者 Wei Shi-long Guo Wei-ping Ji You-qing 《Communications in Mathematical Research》 CSCD 2015年第2期149-160,共12页
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-mappings and prove str... 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-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces. 展开更多
关键词 mixed type asymptotically nonexpansive mapping uniformly convexBanach space common fixed point strong convergence
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INTERATIVE APPROXIMATION OF FIXED POINTS FOR ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES
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作者 曾六川 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第12期1421-1430,共10页
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces... A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings,asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings.The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered.Not only S.S.Chang's inequality but also H.K.Xu's one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one.Moreover,Zhang Shi_sheng's method(Applied Mathematics and Mechanics(English Edition),2001,22(1):25-34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also,the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria.The above results unify,improve and generalize Zhang Shi_sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors. 展开更多
关键词 almost asymptotically nonexpansive type mapping fixed point modified Ishikawa iterative sequence with error modified Mann iterative sequence with error
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COMMON FIXED POINT THEOREM FOR NONCOMMUTING MAPPINGS SATISFYING A GENERALIZED ASYMPTOTICALLY NONEXPANSIVE CONDITION
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作者 P. Vijayaraju R. Hemavathy 《Analysis in Theory and Applications》 2008年第3期211-224,共14页
We present a common fixed point theorem for generalized asymptotically non- expansive and noncommuting mappings in normed linear spaces.
关键词 Cq-commuting generalized asymptotically nonexpansive mapping common fixed point
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Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces
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作者 WANG XIONG-RUI 《Communications in Mathematical Research》 CSCD 2011年第4期369-377,共9页
In this paper, the iteration xn+l =αny + (1 -αn)Ti(n)k(n)xn for a family of asymptotically nonexpansive mappings T1, T2, ..., TN is originally introduced in an uniformly convex Banach space. Motivated by rec... In this paper, the iteration xn+l =αny + (1 -αn)Ti(n)k(n)xn for a family of asymptotically nonexpansive mappings T1, T2, ..., TN is originally introduced in an uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings. 展开更多
关键词 asymptotically nonexpansive mapping sunny nonexpansive retraction uniformly Ggteaux differentiable eeakly sequentially continuous duality
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ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED OINTS FOR ASYMPTOTICALLY NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES 被引量:7
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第1期25-34,共10页
Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained.
关键词 asymptotically nonexpansive mapping fixed point modified Ishikawa iterative sequence with errors modified Mann iterative sequence with errors
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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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Strongly Convergent Approximations to Fixed Points of Total Asymptotically Nonexpansive Mappings 被引量:1
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作者 Yakov ALBER Rafa ESPíNOLA Pepa LORENZO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第6期1005-1022,共18页
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 asy... 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. 展开更多
关键词 asymptotically nonexpansive mappings best approximation fixed point duality map iteration schemes
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Asymptotic Behavior of Asymptotically Nonexpansive Type Mappings in Banach Space 被引量:2
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作者 ZHU Lan Ping LI Gang 《Journal of Mathematical Research and Exposition》 CSCD 2009年第1期129-136,共8页
Let X be a uniformly convex Banach space X such that its dual X^* has the KK property. Let C be a nonempty bounded closed convex subset of X and G be a directed system. Let ={Tt : t ∈ G} be a family of asymptotica... Let X be a uniformly convex Banach space X such that its dual X^* has the KK property. Let C be a nonempty bounded closed convex subset of X and G be a directed system. Let ={Tt : t ∈ G} be a family of asymptotically nonexpansive type mappings on C. In this paper, we investigate the asymptotic behavior of {Ttx0 : t∈ G} and give its weak convergence theorem. 展开更多
关键词 asymptotically nonexpansive type mappings Kadec-Klee property directed system asymptotic behavior.
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ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE 被引量:2
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作者 ZENGLuchuan 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2004年第2期188-196,共9页
Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and l... Let C be a nonempty weakly compact convex subset of a Banach space X, and T : C →C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (i) if X has uniform normal structure and limsup |||TjN||| < N(X)~1/(N(X)) , where|||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point. 展开更多
关键词 mapping of asymptotically nonexpansive type fixed point uniform normal structure weak uniform normal structure uniform convexity in every direction.
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Asymptotic Behavior of Non-Lipschitzian Mappings in Banach Spaces *
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作者 李刚 《Journal of Mathematical Research and Exposition》 CSCD 1998年第3期319-325,共7页
Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space with a Fréchet differentiable norm, and G be a directed system , let T= {T t:t∈G} be asymptotically nonexpansive ty... Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space with a Fréchet differentiable norm, and G be a directed system , let T= {T t:t∈G} be asymptotically nonexpansive type mappings on C . We give the weak convergence theorem of {T t:t∈G} in this paper. 展开更多
关键词 directed system asymptotica behavior asymptotically nonexpansive type mappings.
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Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces 被引量:2
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作者 Ruo Feng RAO 《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期749-756,共8页
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many a... In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings. The main results obtained in this paper improve and extend some recent results. 展开更多
关键词 asymptotically nonexpansive mapping Gauge function weakly continuous duality map.
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ON REICH'S OPEN QUESTION 被引量:1
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第6期646-653,共8页
Under more general form and more general conditions an affirmative answer to Reich's open question is given. The results presented also extend and improve some recent results of Reich, Shioji, Takahashi and Wittmann.
关键词 asymptotically nonexpansive mapping nonexpansive mapping fixed point iterative approximation
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UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION
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作者 曾六川 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第9期1204-1211,共8页
The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive m... The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich' s open question is given. The results presented extend and improve Zhang Shisheng' s recent ones in the following aspects : (i) Zhang' s stronger condition that the sequence of iterative parameters converges to zero is removed; (ii) Zhang' s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; (iii) Zhang' s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann. 展开更多
关键词 asymptotically nonexpansive mapping fixed point uniform normal structure uniformly CJateaux differentiable norm iterative approximation
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Strong Convergence and Certain Control Conditions for Modified Ishikawa Type Iteration
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作者 王学武 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第4期578-584,共7页
In this paper, we establish the strong convergent theorems of an iterative algorithm for asymptotically nonexpansive mappings in Banach spaces and nonexpansive mappings in uniformly smooth Banach spaces, respectively.... In this paper, we establish the strong convergent theorems of an iterative algorithm for asymptotically nonexpansive mappings in Banach spaces and nonexpansive mappings in uniformly smooth Banach spaces, respectively. The results presented in this paper not only give an affirmative partial answer to Reich's open question, but also generalize and improve the corresponding results of Chang, Lee and Chan [7] and Kim and Xu [10] . 展开更多
关键词 asymptotically nonexpansive mapping iterative scheme strong convergence fixed point
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COMMON FIXED POINTS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS
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作者 Sumit Chandok T. D. Narang 《Analysis in Theory and Applications》 2012年第1期1-12,共12页
For a subset K of a metric space (X,d) and x ∈ X,Px(x)={y ∈ K : d(x,y) = d(x,K)≡ inf{d(x,k) : k ∈ K}}is called the set of best K-approximant to x. An element go E K is said to be a best simulta- neous ... For a subset K of a metric space (X,d) and x ∈ X,Px(x)={y ∈ K : d(x,y) = d(x,K)≡ inf{d(x,k) : k ∈ K}}is called the set of best K-approximant to x. An element go E K is said to be a best simulta- neous approximation of the pair y1,y2 E ∈ if max{d(y1,go),d(y2,go)}=inf g∈K max {d(y1,g),d(y2,g)}.In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T- and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas^[1], S. Chandok and T.D. Narang^[2], T.D. Narang and S. Chandok^[11], S.A. Sahab, M.S. Khan and S. Sessa^[14], P. Vijayaraju^[20] and P. Vijayaraju and M. Marudai^[21]. 展开更多
关键词 Banach operator pair best approximation demicompact fixed point STAR-SHAPED nonexpansive asymptotically nonexpansive and uniformly asymptot-ically regular maps
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