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Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

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Applied Mathematics and Mechanics(English Edition) 2009年第7期30卷 925-932页

作者：刘英 College of Mathematics and Computer Hebei University

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

关键词： relatively nonexpansive mapping generalized projection inverse-strongly-monotone variational inequality p-uniformly convex

Modified Block Iterative Method for Solving Convex Feasibility Problem, Equilibrium Problems and Variational Inequality Problems

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Acta Mathematica Sinica,English Series 2012年第4期28卷 741-758页

作者： Shi Sheng ZHANG Chi Kin CHAN H.W.JOSEPH LEE College of Statistics and Mathematics Yunnan Uniersity of Finance and Economics Department of Applied Mathematics The Hong Kong Polytechnic University

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

关键词： Modified block iterative algorithm quasi-φ-asymptotically nonexpansive mapping quasi-φ-nonexpansive mapping relatively nonexpansive mapping generalized projection

MULTI-VALUED TOTALLY QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES

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Acta Mathematica Scientia 2013年第2期33卷 589-599页

作者：张石生王林赵云河 College of Statistics and Mathematics Yunnan University of Finance and Economics

The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.

关键词： Multi-valued totally Quasi-q^-asymptotically nonexpansive semi-groups mod-ified Halpern-Mann-type iteration multi-valued quasi-qS-symptotically nonex-pansive semi-groups multi-valued quasi-~b-nonexpansive semi-groups multi-valued relatively nonexpansive semi-groups generalized projection

Strong Convergence Theorems for a Family of Quasi-φ-Asymptotically Nonexpansive Mappings

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Journal of Mathematical Research and Exposition 2011年第2期31卷 303-314页

作者： King Hui GAO Hai Yun ZHOU College of Mathematics and Computer Science Yah'an University Shaanxi 716000 P. R. China Department of Mathematics People's Liberation Army Ordnance Engineering College Hebei 050003 P. R. China

The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive *** results hold in reflexive,strictly convex,smooth Banach spaces with the property（K）.The results of this paper improve and extend recent some relative results.

关键词： quasi-φ-asymptotically nonexpansive mapping hybrid algorithm generalized projection strong convergence theorem

Weak Convergence of a projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space

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Journal of Mathematical Research and Exposition 2010年第4期30卷 716-724页

作者： Ying LIU College of Mathematics and Computer Hebei University Hebei 071002 P. R. China

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.

关键词： relatively nonexpansive mapping generalized projection inverse-strongly-monotone mapping weakly sequential continuity p-uniformly convexity constant.

Strong Convergence for a Countable Family of Total Quasi-φ-asymptotically Nonexpansive Nonself Mappings in Banach Space

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Communications in Mathematical Research 2015年第1期31卷 31-39页

作者： WANG XIONG-RUI QUAN JING Ji You-qing Institute of Mathematics Yibin University

The purpose of this article is to introduce a class of total quasi-Ф- asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-Ф-asymptotically nonexpan- sive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this article extend and improve the corresponding results of many authors.

关键词： strong convergence total quasi-Ф-asymptoticaily nonexpansive nonself generalized projection

Shrinking projection Methods for a Family of Quasi-φ-Strict Asymptotically Pseudo-Contractions in Banach Spaces

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Journal of Mathematical Research and Exposition 2011年第5期31卷 905-914页

作者： Xing Hui GAO Hai Yun ZHOU College of Mathematics and Computer Science Yan'an University Shaanxi 716000 P. R. China Department of Basic Courses Shijiazhuang Mechanical Engineering College Hebei 050003 P. R. China

The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property （K）. The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.

关键词： strong convergence a family of quasi-φ-strict asymptotically pseudo-contractions generalized projection shrinking projection method Banach spaces.

非线性互补约束规划的一个广义强次可行方向算法

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高等学校计算数学学报 2007年第1期29卷 15-27页

作者：简金宝覃义梁玉梅广西大学数学与信息科学学院南京航空航天大学民航学院上海金融学院应用数学系

1引言本文讨论带非线性互补约束的最优化问题: (MPEC) (?) (1)其中(x,y,w)∈Rn+m+m,f∶Rn+m→R,g=(g1,g2,…,gl)T∶Rn+m→Rl,F= (F1,F2…Fm)T∶Rn+m→Rm均是连续可微的,w⊥y表示向量w和y是正交的,即wTy=0,w ,y∈Rm．记(MPEC)可行集为X．这类问题广泛存在于工程技术、经济、博弈论等各个领域,有着直接的应用价值,故受到人们的广泛关注．关于这方面的应用及部分成果可参考文献[1]-[10]．显然,若将条件F(x,y)⊥y写成内积的形式F(x,y)Ty=0,则(1)成为一个标准的光滑非线性规划问题(SSNP)．从理论上来说,现有的理论、方法和技术应可以解决问题(1)．遗憾的是,文献[4]

关键词： nonlinear complementarity constraints optimization generalized projection strongly subfeasible direction method convergence

Monotone CQ Algorithm of Fixed Points for Weak Relatively Nonexpansive Mappings and Applications

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Journal of Mathematical Research and Exposition 2008年第4期28卷 957-967页

作者：苏永福高俊宇周海云 Department of Mathematics Tianjin Polytechnic University Department of Mathematics Cangzhou Normal College Department of Mathematics Shijiazhuang Mechanical Engineering College

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...

关键词： weak relatively nonexpansive mapping generalized projection asymptotic fixed point monotone CQ method maximal monotone operator.