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NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY L-LIPSCHITZIAN MAPPINGS 被引量:5
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作者 谷峰 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期2058-2066,共9页
The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Bana... The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7]. 展开更多
关键词 asymptotically pseudo-contractive mapping uniformly l-lipschitzian map- ping parallel iterative algorithm
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UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n 被引量:4
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作者 冯淑霞 刘太顺 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期435-443,共9页
In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities... In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them. 展开更多
关键词 uniformly starlike mappings uniformly convex mappings the unit ball
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Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications 被引量:1
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作者 Yi Li 《Applied Mathematics》 2013年第9期6-12,共7页
The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong c... The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497). 展开更多
关键词 MULTI-VALUED mapping Totally Quasi- Ø -Asymptotically NONEXPANSIVE Countable FAMILY of uniformly Totally Quasi- Ø -Asymptotically NONEXPANSIVE MULTI-VALUED mappings Firmly Convergence
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Convergence of Iterative Sequence with Mixed Errors for Uniformly Quasi-Lipschitzian Mappings
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作者 张勇 《Journal of Southwest Jiaotong University(English Edition)》 2005年第2期185-188,共4页
In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special c... In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results. 展开更多
关键词 Convex metric space uniformly quasi-Lipschitzian mapping Ishikawa iterative sequence with mixed eroors Fixed point
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A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism 被引量:4
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作者 王福来 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期244-249,共6页
A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained... A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator. 展开更多
关键词 pseudo random numbers uniform map CHAOS
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A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense
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作者 Godwin Amechi Okeke Austine Efut Ofem 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期248-263,共16页
In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the inte... In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature. 展开更多
关键词 xed point asymptotically genralizedΦ-hemicontractive mapping in the intermediate sense uniformly continuos implicit iteration process strong convergence Banach spaces
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Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第12期1561-1568,共8页
First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of... First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper. 展开更多
关键词 condensing set-valued mapping maximal element generalized game equi-librium locally FC-uniform spaces
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7.0T小动物磁共振成像系统几个常用线圈T1 mapping均匀性研究 被引量:1
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作者 戚鸣 张建平 章英剑 《肿瘤影像学》 2020年第2期175-180,共6页
目的:旨在评估7.0T小动物磁共振成像(magnetic resonance imaging,MRI)几个常用线圈采集T1 mapping的均匀性。方法:分别用大/小鼠脑表面线圈、小鼠头/体部容积线圈测量去离子水、0.2 mmol/L及0.4 mmol/L马根维显溶液的T1mapping,并勾画... 目的:旨在评估7.0T小动物磁共振成像(magnetic resonance imaging,MRI)几个常用线圈采集T1 mapping的均匀性。方法:分别用大/小鼠脑表面线圈、小鼠头/体部容积线圈测量去离子水、0.2 mmol/L及0.4 mmol/L马根维显溶液的T1mapping,并勾画多个感兴趣区(regions of interest,ROI),比较T1 mapping空间均匀性。结果:不同线圈对T1值的测量存在空间均匀性差异,并且特定情况下容积线圈中T1 mapping差异比信号强度差异更灵敏。总体而言,小口径线圈均匀性优于大口径线圈;X方向(左右)均匀性相对较好,优于Y方向(上下)均匀性。结论:建议将T1 mapping均匀性作为质控参考指标之一。采集T1 mapping时尽可能采用小口径线圈。当实验动物采用仰卧或俯卧位时,选取对侧组织T1值作对比具有更高的可信度。 展开更多
关键词 小动物磁共振成像 T1 mapping 均匀性
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STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Huang Jianfeng Wang Yuanheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第3期311-315,共5页
This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty... This paper studies the convergence of the sequence defined by x0 ∈ C, xn+l =αnu+(1-αn)Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results. 展开更多
关键词 nonexpansive mapping uniformly convex Banach space uniformly smooth Banach space Banach limit.
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APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Yekini SHEHU 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期409-423,共15页
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin... Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results. 展开更多
关键词 Pseudo-contractive mappings reflexive Banach spaces uniformly Gateaux differentiable norm variational inequality
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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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ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES
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作者 曾六川 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第3期344-354,共11页
The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in... The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0. 展开更多
关键词 asymptotic regularity common fixed point Lipschitzian mapping p- uniformly convex Banach space weak ω-limit set
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APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS
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作者 Eric U.OFOEDU Charles E.ONYI 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期1225-1240,共16页
It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Ban... It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gateaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly G&teaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore, Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results. 展开更多
关键词 nonexpansive mappings reflexive real Banach spaces fixed point uniformly Aateaux differentiable norm
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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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A new iterative process for approximating common fixed points of nonself I-asymptotically quasi-nonexpansive mappings
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作者 Isa Yildirim Feng Gu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2012年第4期489-502,共14页
In this paper, we introduce an iterative process for two nonself I-asymptotically quasi-nonexpansive mappings and two finite families of such mappings in Banach spaces, and prove some strong convergence theorems for s... In this paper, we introduce an iterative process for two nonself I-asymptotically quasi-nonexpansive mappings and two finite families of such mappings in Banach spaces, and prove some strong convergence theorems for such mappings. Our results extend some existing results. 展开更多
关键词 nonseIf I-asymptoticaliy quasi-nonexpansive mapping common fixed point uniformly convexBanach space.
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Picard Approximation of Fixed Points of Nonexpansive Mappings
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作者 黄家琳 《Journal of Southwest Jiaotong University(English Edition)》 2003年第2期189-191,共3页
Let C be a bounded convex subset in a uniformly convex Banach space X, x 0, u n∈C , then x n+1 =S nx n, where S n=α n0 I+α n1 T+α n2 T 2+…+α nk T k+γ nu n, α ni ≥0, 0<α≤α ... Let C be a bounded convex subset in a uniformly convex Banach space X, x 0, u n∈C , then x n+1 =S nx n, where S n=α n0 I+α n1 T+α n2 T 2+…+α nk T k+γ nu n, α ni ≥0, 0<α≤α n0 ≤b<1, ∑ki=0α ni +γ n=1, and n≥1. It is proved that x n converges to a fixed point on T if T is a nonexpansive mapping. 展开更多
关键词 nonexpansive mapping uniformly convex space iteration process
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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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Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple Singularities
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作者 Hyunju Kim 《Journal of Applied Mathematics and Physics》 2019年第7期1572-1598,共27页
In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the ... In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0?space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities. 展开更多
关键词 mapping Method NON-uniform Rational B-SPLINE (NURBS) GALERKIN Approximation Isogeometric Analysis MULTIPLE SINGULARITIES
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Approximation of fixed points of strict Hemi-contraction mapping
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作者 Tang Chunlei, male, 33 years old, associate professor. Tang Chunlei, Deng Lei Department of Mathematics, Southwest China Normal University, Chongqing 400715 《西南师范大学学报(自然科学版)》 CAS CSCD 北大核心 1998年第5期7-10,共4页
Lemma1[1]IfEisauniformlysmoothBanachspace,thereexistsacontinuousnondecreasingfunctionβ(t):[0,∞)→[0,∞)suchth... Lemma1[1]IfEisauniformlysmoothBanachspace,thereexistsacontinuousnondecreasingfunctionβ(t):[0,∞)→[0,∞)suchthatlimt→0+β(t)=0,β... 展开更多
关键词 hemi CONTRACTION mapping ITERATION methods uniformly smooth BANACH space
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