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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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Common Fixed Point Iterations of Generalized Asymptotically Quasi-Nonexpansive Mappings in Hyperbolic Spaces
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作者 A. R. Khan H. Fukhar-ud-din 《Journal of Applied Mathematics and Physics》 2014年第5期170-175,共6页
We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-st... We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously. 展开更多
关键词 HYPERBOLIC Space general ITERATIVE Method generalized ASYMPTOTICALLY quasi-nonexpansive mapping 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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Fixed Point Theorem of{a, b, c}Contraction and Nonexpansive Type Mappings in Weakly Cauchy Normed Spaces
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作者 Sahar Mohamed Ali 《Analysis in Theory and Applications》 2013年第3期280-288,共9页
Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectiv... Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following: 1. If T is {a,b,c}-ntype mapping, then inf{ || T(x)-x|| :x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞||T(xn) - Xn|| = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn (x)}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13]. 展开更多
关键词 fixed point generalized type of contaction and nonexpansive mappings normed space.
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Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems 被引量:1
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作者 Lijun Chen Jianhua Huang 《Applied Mathematics》 2011年第10期1213-1220,共8页
In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of non... In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions. 展开更多
关键词 generalized Mixed EQUILIBRIUM Problem Hybrid ITERATIVE Scheme fixed point nonexpansive mapping STRONG Convergence
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Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered <i>G</i>-Partial Metric Spaces
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作者 Johnson O. Olaleru Kanayo Stella Eke Hallowed O. Olaoluwa 《Applied Mathematics》 2014年第6期1004-1012,共9页
We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent result... We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent results in literature. 展开更多
关键词 fixed points generalized quasi-Contraction maps Bounded Orbit Partially ORDERED Set G-Partial Metric Spaces
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Quadratic minimization for equilibrium problem variational inclusion and fixed point problem
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作者 张石生 李向荣 陈志坚 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第7期917-928,共12页
The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating ... The purpose of this paper is to find the solutions to the quadratic mini- mization problem by using the resolvent approach. Under suitable conditions, some new strong convergence theorems are proved for approximating a solution of the above min- imization problem. The results presented in the paper extend and improve some recent results. 展开更多
关键词 quadratic minimization generalized equilibrium fixed point variational inclusion multi-valued maximal monotone mapping inverse-strongly monotone mapping resolvent operator nonexpansive mapping
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Monotone CQ Algorithm of Fixed Points for Weak Relatively Nonexpansive Mappings and Applications
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作者 苏永福 高俊宇 周海云 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第4期957-967,共11页
Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to... Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushi... 展开更多
关键词 weak relatively nonexpansive mapping generalized projection asymptotic fixed point monotone CQ method maximal monotone operator.
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CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES 被引量:3
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作者 TIAN You-xian(田有先) +1 位作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1001-1008,共8页
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding r... Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces. 展开更多
关键词 convex metric space fixed point generalized Ishikawa (Mann) iterative sequence with errors general quasi-contractive mapping
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Generalized Ⅰ-Nonexpansive Selfmaps and Invariant Approximations 被引量:1
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作者 M.A.AL-THAGAFI Naseer SHAHZAD 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第5期867-876,共10页
Common fixed point results for new classes of noncommuting selfmaps satisfying generalized I-contraction or I-nonexpansive type conditions are established. We apply them to obtain several invariant approximation resul... Common fixed point results for new classes of noncommuting selfmaps satisfying generalized I-contraction or I-nonexpansive type conditions are established. We apply them to obtain several invariant approximation results which unify, extend, and complement the well-known results. 展开更多
关键词 common fixed point occasionally weakly compatible map ultraoccasionally weakly compatible map generalized I-nonexpansive map invariant approximation
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A SOLUTION OF A GENERAL EQUILIBRIUM PROBLEM 被引量:1
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作者 H.R.SAHEBI A.RAZANI 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1598-1614,共17页
Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semig... Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper. 展开更多
关键词 nonexpansive semigroup general equilibrium problems strongly positivelinear bounded operator or-inverse strongly monotone mapping fixed point Hilbert space
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SOME GENERALIZATIONS OF KY FAN'S BEST APPROXIMATION THEOREM
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作者 A.R.Khan N.Hussain A.B.Thaheem 《Analysis in Theory and Applications》 2004年第2期189-198,共10页
We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map stud... We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory. 展开更多
关键词 best approximation fixed point * -nonexpansive multivalued map almost quasi-convex function metrizable topological vector space hyperconvex space
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广义准(16)类非扩张映射的不动点定理 被引量:1
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作者 杜成林 朴永俊 于声雷 《哈尔滨师范大学自然科学学报》 CAS 1991年第4期9-12,共4页
本文引入广义准(16)类非扩张映射的新概念,利用广义Chebysev 中心建立了这类映射的新的不动点定理。
关键词 不动点 非扩张映射 Chebysev中心
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Banach空间中一类分裂等式可行问题的强收敛定理
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作者 陈丽君 程丽 《宁夏大学学报(自然科学版)》 CAS 2023年第4期317-322,共6页
为了在Banach空间中得到分裂等式公共不动点问题的强收敛性,在适当的条件下构造了一种新的迭代算法,并在更具一般性的条件下证明了由该算法生成的序列强收敛于分裂等式不动点问题的一个解.最后,根据所得结论进一步得到了分裂等式均衡问... 为了在Banach空间中得到分裂等式公共不动点问题的强收敛性,在适当的条件下构造了一种新的迭代算法,并在更具一般性的条件下证明了由该算法生成的序列强收敛于分裂等式不动点问题的一个解.最后,根据所得结论进一步得到了分裂等式均衡问题与极大单调算子零点问题的强收敛性定理. 展开更多
关键词 分裂等式不动点问题 BANACH空间 拟非扩张映射 强收敛
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双曲空间中渐近拟非扩张映射与几乎渐近拟非扩张映射混合迭代的强收敛
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作者 刘涌泉 李刚 方达 《高师理科学刊》 2023年第12期9-14,共6页
在双曲空间中,引入了关于三个渐近拟非扩张映射和三个几乎渐近拟非扩张映射新的SP-迭代算法,获得了渐近拟非扩张映射和几乎渐近拟非扩张映射在新的SP-迭代算法下的强收敛性定理,所得结果推广和改进了相关文献的结论.
关键词 双曲空间 渐近拟非扩张映射 几乎渐近拟非扩张映射 SP-迭代算法 公共不动点
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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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有限族广义一致伪Lipschitz映象公共不动点的迭代收敛性 被引量:16
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作者 赵美娜 张树义 赵亚莉 《烟台大学学报(自然科学与工程版)》 CAS 2017年第1期7-10,60,共5页
目的是在Banach空间中引入并研究一类广义一致伪Lipschitz映象,举例说明这种映象的广泛性,并在一定条件下,证明了一族广义一致伪Lipschitz映象公共不动点的带误差的多步迭代序列收敛的充分必要条件,从而改进与推广了一些已知的结果.获... 目的是在Banach空间中引入并研究一类广义一致伪Lipschitz映象,举例说明这种映象的广泛性,并在一定条件下,证明了一族广义一致伪Lipschitz映象公共不动点的带误差的多步迭代序列收敛的充分必要条件,从而改进与推广了一些已知的结果.获得的收敛准则丰富了非线性算子不动点的迭代逼近理论. 展开更多
关键词 一致伪Lipschitz映象 广义一致伪Lipschitz映象 公共不动点 多步迭代序列
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Banach空间中的渐近拟非扩张型映象不动点的具混合误差的Ishikawa迭代逼近问题 被引量:9
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作者 王绍荣 杨泽恒 《西南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2004年第4期578-581,共4页
在更一般的条件下研究了Banach空间中渐近拟非扩张型映象的具误差或混合误差的Ishikawa迭代序列强收敛到其不动点的充分必要条件.
关键词 拟非扩张映象 渐近拟非扩张映象 混合误差 ISHIKAWA迭代序列 不动点
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2个有限族广义依中心意义的渐近非扩张非自映像公共不动点定理 被引量:6
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作者 王元恒 石惠敏 《浙江大学学报(理学版)》 CAS CSCD 2014年第3期282-287,共6页
在任意实的Banach空间中,对于2个有限族广义依中心意义的渐近非扩张非自映像,引入了一种新的带误差修正的广义Ishikawa迭代序列.并在适当条件下,多次巧妙地应用数学归纳法等工具,证明了该迭代序列强收敛于2个映像族的公共不动点.其结果... 在任意实的Banach空间中,对于2个有限族广义依中心意义的渐近非扩张非自映像,引入了一种新的带误差修正的广义Ishikawa迭代序列.并在适当条件下,多次巧妙地应用数学归纳法等工具,证明了该迭代序列强收敛于2个映像族的公共不动点.其结果改进和推广了近代许多相关的结果. 展开更多
关键词 广义依中心意义渐近非扩张非自映像 带误差修正的广义Ishikawa迭代序列 不动点 强收敛
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广义渐近拟非扩张映射修正隐迭代过程的强收敛(英文) 被引量:6
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作者 钟小毛 邓磊 《西南大学学报(自然科学版)》 CAS CSCD 北大核心 2009年第2期20-24,共5页
证明了巴拿赫空间中修正的隐迭代序列强收敛到有限个广义渐近拟非扩张映射的公共不动点的几个定理.
关键词 隐迭代过程 渐近拟非扩张映射 公共不动点
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