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THREE-STEP ITERATIONS FOR nonexpansive mappingS AND INVERSE-STRONGLY MONOTONE mappingS

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Journal of Systems Science & Complexity 2009年第2期22卷 333-344页

作者： Meijuan SHANG Yongfu SU Xiaolong QIN Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Department of Mathematics Shijiazhuang University Shijiazhuang 050035 China Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China. Department of Mathematics and the Research Institute of Natural Sciences Gyeongsang National UniversityChinju 660-701 Korea.

This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert *** authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational ***,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone *** results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.

关键词： Inverse-strongly monotone mapping metric projection nonexpansive mapping variational inequality.

ON THE PROBLEM OF DISSIPATIVE PERTURBATIONS OF nonexpansive mappingS

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Applied Mathematics and Mechanics(English Edition) 2001年第4期22卷 478-482页

作者： LUO Yuan-song(罗元松) Department of Mathematics Yibin Teachers'' CollegeYibin 644007 P R China

Some Fixed point theorems for mappings of the type - A + T are established, where P is a cone in a Hilbert space, A: P --> 2(P) is an accretive mappings and T: P --> P is a nonexpansive mappings. In application, the results presented in the paper are used to study the existence problem of solutions far a class of nonlinear integral equations in L-2 (Omega).

关键词： nonexpansive mapping accretive mapping fixed point theorem nonlinear integral equation

How to Recognize nonexpansive mappings and Isometric mappings

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Acta Mathematica Sinica,English Series 2011年第10期27卷 1959-1966页

作者： Guang Gui DING Yu Mei MA School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 P. R. China Department of Applied Mathematics Dalian Nationality University Liaoning 116600 P. R. China

In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.

关键词： nonexpansive mapping smooth point weak*-compact set

A Riemannian Inertial Mann Algorithm for nonexpansive mappings on Hadamard Manifolds

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Numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 954-967页

作者： Teng-Teng Yao Xiao-Qing Jin Zhi Zhao Department of Mathematics School of SciencesZhejiang University of Science and TechnologyHangzhou 310023China Department of Mathematics University of MacaoMacao 999078SARChina Department of Mathematics School of SciencesHangzhou Dianzi UniversityHangzhou 310018China

The problem of finding fixed points of nonexpansive mappings on Hadamard manifolds is considered in this *** solve this kind of problem,we propose a modified Riemannian Mann algorithm with inertial *** the assumption of existence of fixed points of the nonexpansive mapping,the global convergence of the proposed algorithm is *** show the efficiency of the proposed algorithm,numerical comparisons with some existing algorithms are reported.

关键词： nonexpansive mapping Hadamard manifold fixed point inertial Mann algorithm

STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR nonexpansive mappingS IN BANACH SPACES

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Applied Mathematics(A Journal of Chinese Universities) 2007年第3期22卷 311-315页

作者： Huang Jianfeng Wang Yuanheng Dept. of Math. Zhejiang Normal Univ. Jinhua 321004 China

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.

关键词： nonexpansive mapping uniformly convex Banach space uniformly smooth Banach space Banach limit.

Ishikawa Iteration Process for Approximating Fixed Points of nonexpansive mappings

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Journal of Mathematical Research and Exposition 2003年第1期23卷 33-39页

作者：曾六川上海师范大学数学系上海200234

Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable *** C be a bounded closed convex subset of ***:C→C is a nonexpansive *** for any initial data x0∈C,the Ishikawaiteration process{xn},defined by xn=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,converges weakly to a fixed point of T,where{tn}and{sn}are sequences in[0,1]withsome restrictions.

关键词： fixed point nonexpansive mapping Ishikawa iteration process uniformly convex Banach space.

Algorithm for solving a class of general mixed variational inequalities and nonexpansive mappings in Hilbert spaces

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商丘师范学院学报 2010年第3期26卷 18-22页

作者： ZHAI Guangfu FAN Liya School of Mathematics Science Liaocheng University Liaocheng 252059 China

This paper is devoted to study the convergence of a new class of generalized system for variational *** results presented in this paper modify and improve the recent result announced by Chang.[***,*** Lee,Generalzed s... 详细信息

关键词： H-monotone operator resolvent operator technique variational inclusion nonexpansive mapping

Picard Approximation of Fixed Points of nonexpansive mappings

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Journal of Southwest Jiaotong University(English Edition) 2003年第2期11卷 189-191页

作者：黄家琳 Department of Mathematics Yibin University

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 ... 详细信息

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, 0nonexpansive mapping.

关键词： nonexpansive mapping uniformly convex space iteration process

STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES

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Journal of Systems Science & Complexity 2008年第3期21卷 474-482页

作者： Yongfu SU Xiaolong QIN Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China

K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonex-pansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial＇s condition.

关键词： Hybrid method nonexpansive mapping nonexpansive semigroup proximal point algorithm strong convergence