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工程数学学报 1991年第2期8卷 19-30页

作者： Xu Hong-KunInstitute of Applied Mathematics, East China University of Chemical Technology, Changhai 200237, China

Let C be a closed bounded convex subset of a uniformaly convex Banach space X with a Frechet differentiable norm, F= {T(t):t ≥0} an asymptotically noncxpansivc semigroup on C, and u:[0,∞)→ C an almost-orbit of F. Then we show that {u(t):t ≥ 0} is almost convergent weakly to a common fixed point y of F, that isweak - lim1/tdr - y uniformly in s≥ *** implies that {u(t):t≥ 0} converges weakly to y if and onlyif u is weakly asymptotically regular, i.e lim (u(t + s) - u(t) = 0 weakly for all s≥ 0.

关键词： Almost-orbit asymptotically nonexpansive semigroup almost convergence fixed point nonexpansive retraction.

Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically nonexpansive Semigroups

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Advances in Pure Mathematics 2014年第6期4卷 244-252页

作者： Hongbo Liu Yi Li School of Science Southwest University of Science and Technology Mianyang China

Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

关键词： Hybrid Iterative Algorithm Uniformly Asymptotically nonexpansive Semigroups Equilibrium Problem Common Fixed Point

An Iterative Algorithm for Generalized Mixed Equilibrium Problems and Fixed Points of nonexpansive Semigroups

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Journal of Applied Mathematics and Physics 2017年第2期5卷 276-293页

作者： Jong Kyu Kim Salahud din Won Hee Won Hee Department of Mathemarics Education Kyungnam University Changwon Gyeongnam Korea Department of Mathematics Jazan University Jazan Kingdom of Saudi Arabia

In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener... 详细信息

关键词： Meir-Keeler Contraction Mappings Left Regular Generalized Mixed Equilibrium Problems Variational Inequalities α-Inverse Strongly Monotone Mappings nonexpansive Semigroups

Approximation of Common Fixed Points of Pointwise Asymptotic nonexpansive Maps in a Hadamard Space

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Advances in Pure Mathematics 2012年第6期2卷 450-456页

作者： Safeer Hussain Khan H. Fukhar-ud-din Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran KSA Department of Mathematics Statistics and Physics Qatar University Doha Qatar

We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely (Cn(x)-1)< to answer in the affirma-tive to the open question posed by Tan and Xu [1] even in a general setup.

关键词： Pointwise Asymptotic nonexpansive Map Common Fixed Point Ishikawa Iteration Process Strong Convergence Weak Convergence

Common Fixed Point Theorems for Totally Quasi-G-Asymptotically nonexpansive Semigroups with the Generalized f-Projection

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Applied Mathematics 2014年第1期5卷 25-34页

作者： Chunjie Wang Yuanheng Wang Department of Mathematics Zhejiang Normal University Jinhua China

In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.

关键词： Totally Quasi-G-Asymptotically nonexpansive Semigroup Generalized f-Projection Operator Modified Halpern Type Hybrid Iterative Algorithm Strong Convergence Theorem

Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

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Applied Mathematics 2013年第9期4卷 6-12页

作者： Yi Li School of Science Southwest University of Science and Technology Mianyang China

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).

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

Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems

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Applied Mathematics 2011年第10期2卷 1213-1220页

作者： Lijun Chen Jianhua Huang 不详

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... 详细信息

关键词： Generalized Mixed Equilibrium Problem Hybrid Iterative Scheme Fixed Point nonexpansive Mapping Strong Convergence

Strong Convergence of a General Iterative Algorithm for Mixed Equilibrium, Variational Inequality and Common Fixed Points Problems

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Advances in Pure Mathematics 2013年第1期3卷 83-98页

作者： Tanakit Thianwan Department of Mathematics School of Science University of Phayao Phayao Thailand

The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.

关键词： nonexpansive Mapping Mixed Equilibrium Problem Variational Inequality Common Fixed Points Strong Convergence

On Some Fixed Point Theorems for 1-Set Weakly Contractive Multi-Valued Mappings with Weakly Sequentially Closed Graph

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Advances in Pure Mathematics 2011年第4期1卷 163-169页

作者： Afif Ben Amar Aneta Sikorska-Nowak 不详

In this paper we prove Leray-Schauder and Furi-Pera types fixed point theorems for a class of multi-valued mappings with weakly sequentially closed graph. Our results improve and extend previous results for weakly sequentially closed maps and are very important in applications, mainly for the investigating of boundary value problems on noncompact intervals.

关键词： Measures of Weak Noncompactness Weakly Condensing Weakly nonexpansive

COMMON FIXED POINTS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

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Analysis in Theory and Applications 2012年第1期28卷 1-12页

作者： Sumit Chandok T. D. Narang Guru Nanak Dev University India

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].

关键词： Banach operator pair best approximation demicompact fixed point star-shaped nonexpansive asymptotically nonexpansive and uniformly asymptot-ically regular maps