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Generalized Krasnoselskii-Mann-Type Iteration for Nonexpansive Mappings in banach spaces

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Journal of the Operations Research Society of China 2021年第1期9卷 195-206页

作者： You-Cai Zhang Ke Guo Tao Wang School of Mathematics and Information China West Normal UniversityNanchong 637002SichuanChina

The Krasnoselskii-Mann iteration plays an important role in the approximation of fixed points of nonexpansive mappings,and it is well known that the clas-sic Krasnoselskii-Mann iteration is weakly convergent in Hilbert *** weak convergence is also known even in banach ***,Kanzow and Shehu pro-posed a generalized Krasnoselskii-Mann-type iteration for nonexpansive mappings and established its convergence in Hilbert *** this paper,we show that the generalized Krasnoselskii-Mann-type iteration proposed by Kanzow and Shehu also converges in banach *** applications,we proved the weak convergence of generalized proximal point algorithm in the uniformly convex banach spaces.

关键词： Krasnoselskii-Mann-type iteration Nonexpansive mappings Weak convergence Accretive operator proximal pointalgorithm banach spaces

On Absolute Uniform Retracts, Uniform Approximation Property and Super Weakly Compact Sets of banach spaces

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Acta Mathematica Sinica,English Series 2021年第5期37卷 731-739页

作者： Li Xin CHENG Qing Jin CHENG Jian Jian WANG School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China

In this paper,we show that every super weakly compact convex subset of a banach space is an absolute uniform retract,and that it also admits the uniform compact approximation *** can be regarded as extensions of Linde... 详细信息

关键词： Super weak compactness absolute uniform retract banach spaces

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in banach spaces

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Applied Mathematics and Mechanics(English Edition) 2009年第1期30卷 1-12页

作者：丁协平王中宝 College of Mathematics and Software Science Sichuan Normal UniversityChengdu 610066 P. R. China

A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.

关键词： H-η-monotone operators resolvent operator technique system of set-valued mixed quasi-variational-like inclusions iterative algorithm banach spaces

Viscosity Approximation Methods for Nonexpansive Multimaps in banach spaces

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Acta Mathematica Sinica,English Series 2010年第6期26卷 1165-1176页

作者： Habtu ZEGEYE Naseer SHAHZAD Bahir Dar University Department of Mathematics King Abdul Aziz University

We prove strong convergence of the viscosity approximation process for nonexpansive nonself multimaps. Furthermore, an explicit iteration process which converges strongly to a fixed point of multimap T is constructed.... 详细信息

关键词： nonexpansive retract banach spaces fixed point inwardness nonexpansive multimap

The best approximation theorems and variational inequalities for discontinuous mappings in banach spaces

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Science China Mathematics 2015年第12期58卷 2581-2592页

作者： LIU LiShan KONG DeZhou WU YongHong School of Mathematical Sciences Qufu Normal University Department of Mathematics and Statistics Curtin University of Technology College of Information Science and Engineering Shandong Agricultural University

We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.

关键词： best approximation theorem variational inequality discontinuous map Ky Fan’s theorem fixed point banach spaces

Strongly Irreducible Operators on banach spaces

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Acta Mathematica Sinica,English Series 2012年第4期28卷 727-740页

作者： Yun Nan ZHANG Huai Jie ZHONG School of Mathematics and Computer Science Fujian Normal University Mathematics and Information Science College Hebei Normal University

This paper firstly discusses the existence of strongly irreducible operators on banach spaces. It shows that there exist strongly irreducible operators on banach spaces with w＊-separable dual. It also gives some properties of strongly irreducible operators on banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional banach space, then T is not of finite rank and T is not an algebraic operator. On banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.

关键词： banach spaces strongly irreducible operators w*-separable quasisimilar

The Connection Between the Metric and Generalized Projection Operators in banach spaces

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Acta Mathematica Sinica,English Series 2007年第6期23卷 1109-1120页

作者： Yakov ALBER Jin Lu LI Department of Mathematics Technion Israel Institute of Technology 32000 Haifa Israel Department of Mathematical Sciences Shawnee State University Portsmouth Ohio 45662 USA

In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive banach spaces.

关键词： banach spaces normalized duality mappings metric and generalized projection operators,variational inequalities minimization problems closed and convex subsets and cones

Additive Maps Preserving Similarity of Operators on banach spaces

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Acta Mathematica Sinica,English Series 2006年第1期22卷 179-186页

作者： Jin Chuan HOU Xiu Ling ZHANG Department of Mathematics Shanxi Teachers University Linfen 041004 P R. China

Let X be an infinite-dimensional complex banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.

关键词： Additive maps on operator algebras Similarity of operators banach spaces

Solvability of Impulsive Neutral Functional Differential Inclusions in banach spaces

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Transactions of Tianjin University 2008年第1期14卷 55-60页

作者：任仙玲刘辉昭 School of Management Tianjin University School of Science Hebei University of Technology

Impulsive neutral differential inclusions play an important role in characterizing many social, physical and engineering problems, and the existence of solutions for the initial value problem in banach spaces has been extensively studied. However, in most cases, the nonlinear term on the right-hand side of differential inclusions has to satisfy the compact or continuous assumptions. The object of this paper is to study the existence of solutions to the initial value problems of the first and second order impulsive neutral functional differential inclusions in banach spaces under some weaker conditions, where the nonlinear term on the right-hand side does not necessarily satisfy the compact and continuous assumptions. Based on a fixed point theorem for discontinuous multivalued increasing operators, the results are obtained by means of the partial ordering method and measure of noncompactness.

关键词： impulsive differential inclusions multivalued map fixed point banach spaces