检索结果-内蒙古大学图书馆

New general systems of set-valued variational inclusions involving relative (A, η)-maximal monotone operators in Hilbert spaces

引用

JOURNAL OF INEQUALITIES AND APPLICATIONS 2014年第1期2014卷 1-16页

作者： Xiong, Ting-jian Lan, Heng-you Sichuan Univ Sci & Engn Inst Nonlinear Sci & Engn Comp Zigong 643000 Sichuan Peoples R China Key Lab Higher Educ Sichuan Prov Enterprise Infor Zigong 643000 Sichuan Peoples R China

The purpose of this paper is to introduce and study a class of new general systems of set-valued variational inclusions involving relative (A, eta)-maximal monotone operators in Hilbert spaces. By using the generalized resolvent operator technique associated with relative (A, eta)-maximal monotone operators, we also construct some new iterative algorithms for finding approximation solutions to the general systems of set-valued variational inclusions and prove the convergence of the sequences generated by the algorithms. The results presented in this paper improve and extend some known results in the literature.

关键词： general system of set-valued variational inclusions relative (A, eta)-maximal monotone operator generalized resolvent operator technique relative relaxed cocoercive iterative algorithm convergence criteria

来源：评论

学校读者我要写书评

暂无评论

Solution sensitivity of generalized nonlinear parametric (A, η, m)-proximal operator system of equations in Hilbert spaces

引用

JOURNAL OF INEQUALITIES AND APPLICATIONS 2014年第1期2014卷 1-17页

作者： Kim, Jong Kyu Lan, Heng-you Cho, Yeol Je Kyungnam Univ Dept Math Educ Chang Won 631701 Gyeongnam South Korea Sichuan Univ Sci & Engn Dept Math Zigong 643000 Sichuan Peoples R China Artificial Intelligence Key Lab Sichuan Prov Zigong 643000 Sichuan Peoples R China Gyeongsang Natl Univ Dept Math Educ Chinju 660701 South Korea Gyeongsang Natl Univ RINS Chinju 660701 South Korea King Abdulaziz Univ Dept Math Jeddah 21589 Saudi Arabia

By using the new parametric resolvent operator technique associated with (A, eta, m)-monotone operators, the purpose of this paper is to analyze and establish an existence theorem for a new class of generalized nonlinear parametric (A, eta, m)-proximal operator system of equations with non-monotone multi-valued operators in Hilbert spaces. The results presented in this paper generalize the sensitivity analysis results of recent work on strongly monotone quasi-variational inclusions, nonlinear implicit quasi-variational inclusions, and nonlinear mixed quasi-variational inclusion systems in Hilbert spaces.

关键词： sensitivity analysis relaxed cocoercive operator (A, eta, m)-monotone variational inclusion system (A, eta, m)-proximal operator equation generalized resolvent operator technique

来源：评论

学校读者我要写书评

暂无评论

Graph-convergent analysis of over-relaxed (A, η, m)-proximal point iterative methods with errors for general nonlinear operator equations

引用

FIXED POINT THEORY AND APPLICATIONS 2014年第1期2014卷 161-161页

作者： Lan, Heng-you Sichuan Univ Sci Engn Inst Nonlinear Sci & Engn Comp Zigong 643000 Sichuan Peoples R China Artificial Intelligence Key Lab Sichuan Prov Zigong 643000 Sichuan Peoples R China

In this paper, we introduce and study a new class of over-relaxed (A, eta, m)-proximal point iterative methods with errors for solving general nonlinear operator equations in Hilbert spaces. By using Liu's inequality and the generalized resolvent operator technique associated with (A, eta, m)-monotone operators, we also prove the existence of solution for the nonlinear operator inclusions and discuss the graph-convergent analysis of iterative sequences generated by the algorithm. Furthermore, we give some examples and an application for solving the open question (2) due to Li and Lan (Adv. Nonlinear Var. Inequal. 15(1):99-109, 2012). The numerical simulation examples are given to illustrate the validity of our results.

关键词： new over-relaxed proximal point iterative methods with error general nonlinear operator inclusion (A, eta, m)-monotonicity framework generalized resolvent operator technique graph-convergent analysis

来源：评论

学校读者我要写书评

暂无评论

General hybrid (A, η, m)-proximal point algorithm frameworks for finding common solutions of nonlinear operator equations and fixed point problems

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2013年第4期18卷 895-904页

作者： Lan, Heng-You Cai, Lecai Wu, Shulin Sichuan Univ Dept Math Chengdu 610064 Sichuan Peoples R China Sichuan Univ Sci & Engn Dept Math Zigong 643000 Sichuan Peoples R China

In this paper, we introduce and study a new general class of hybrid (A, eta, m)-proximal point algorithm frameworks for finding the common solutions of nonlinear operator equations and fixed point problems of Lipschitz continuous operators in Hilbert spaces. Further, by using the generalized resolvent operator technique associated with (A, eta, m)-maximal monotone operators, we discuss the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm frameworks. Finally, using software Matlab 7.0, the numerical simulation examples are given to illustrate the validity of main results presented in this paper. (C) 2012 Elsevier B.V. All rights reserved.

关键词： (A, eta, m)-maximal monotonicity General hybrid (A, eta, m)-proximal point algorithm framework System of nonlinear operator equations and fixed point problem generalized resolvent operator technique Solvability and convergence

来源：评论

学校读者我要写书评

暂无评论

New approximation-solvability of general nonlinear operator inclusion couples involving (A,η,m)-resolvent operators and relaxed cocoercive type operators

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2012年第4期17卷 1844-1851页

作者： Lan, Heng-you Cui, Yi-shun Fu, Yu Sichuan Univ Sci & Engn Zigong Dept Math Zigong 643000 Sichuan Peoples R China Sichuan Univ Sci & Engn Zigong Coll Mat & Chem Engn Zigong 643000 Sichuan Peoples R China

In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A,eta,m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A,eta,m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. (C) 2011 Elsevier B.V. All rights reserved.

关键词： generalized resolvent operator technique General nonlinear operator inclusion couple (A,eta,m)-resolvent operators and relaxed cocoercive type operators New perturbed iterative algorithm framework with errors Variational graphical convergence

来源：评论

学校读者我要写书评

暂无评论

Graphical approximation of common solutions to generalized nonlinear relaxed cocoercive operator equation systems with (A, η)-accretive mappings

引用

FIXED POINT THEORY AND APPLICATIONS 2012年第1期2012卷 1-14页

作者： Li, Fang Lan, Heng-you Cho, Yeol Je Sichuan Univ Sci & Engn Dept Math Zigong 643000 Sichuan Peoples R China Gyeongsang Natl Univ Coll Educ Dept Math Educ Chinju 660701 South Korea Gyeongsang Natl Univ Coll Educ RINS Chinju 660701 South Korea

In this paper, we develop a new perturbed iterative algorithm framework with errors based on the variational graphical convergence of operator sequences with (A, eta)-accretive mappings in Banach space. By using the generalized resolvent operator technique associated with (A, eta)-accretive mappings, we also prove the existence of solutions for a class of generalized nonlinear relaxed cocoercive operator equation systems and the variational convergence of the sequence generated by the perturbed iterative algorithm in q-uniformly smooth Banach spaces. The obtained results improve and generalize some well-known results in recent literatures. 2000 Mathematics Subject Classification: 47H05;49J40.

关键词： (A, eta)-accretive mapping generalized resolvent operator technique generalized nonlinear relaxed cocoercive operator equation systems New perturbed iterative algorithm with errors Variational graphical convergence

来源：评论

学校读者我要写书评

暂无评论

Sensitivity analysis for cocoercively monotone variational inclusions and (A, eta)-maximal monotonicity

引用

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2008年第1-2期26卷 281-293页

作者： Mohapatra, Ram N. Verma, Ram U. Univ Cent Florida Dept Math Orlando FL 32816 USA

Sensitivity analysis for cocoercively monotone variational inclusions based on the generalized resolvent operator technique is discussed. The notion of the cocoercive monotonicity unifies most of the existing notions, such as cocoercivity, strong monotonicity, relaxed monotonicity, relaxed cocoercivity, and others. As a result, the obtained results are general in nature.

关键词： Sensitivity analysis Quasivariational inclusions Maximal relaxed monotone mapping (A,eta)-maximal monotone mapping Cocoercively monotone mapping generalized resolvent operator technique

来源：评论

学校读者我要写书评

暂无评论

Sensitivity analysis for generalized strongly monotone variational inclusions based on the (A, η)-resolvent operator technique

引用

APPLIED MATHEMATICS LETTERS 2006年第12期19卷 1409-1413页

作者： Verma, R. U. Univ Toledo Dept Math Toledo OH 43606 USA

Sensitivity analysis for generalized strongly monotone variational inclusions based on the (A, eta)-resolvent operator technique is investigated. The results obtained encompass a broad range of results. (C) 2006 Elsev... 详细信息

关键词： sensitivity analysis quasivariational inclusions maximal relaxed monotone mapping (A, n)-monotone mapping generalized resolvent operator technique

来源：评论

学校读者我要写书评

暂无评论

generalized implicit variational-like inclusion problems involving G-η-monotone mappings

引用

APPLIED MATHEMATICS LETTERS 2007年第2期20卷 216-221页

作者： Zhang, Qing-Bang Beijing Univ Technol Coll Appl Sci Beijing 100022 Peoples R China

A new class of G-eta-monotone mappings is introduced and studied in Hilbert space. By using the properties of G-eta-monotone mappings, the solvability of a class of nonlinear variational inclusions using the generaliz... 详细信息

关键词： G-eta-monotone mappings generalized resolvent operator technique generalized implicit variational-like inclusion

来源：评论

学校读者我要写书评

暂无评论

General nonlinear variational inclusion problems involving A-monotone mappings

引用

APPLIED MATHEMATICS LETTERS 2006年第9期19卷 960-963页

作者： Verma, Ram U. Univ Toledo Dept Math Toledo OH 43606 USA

Based on the notion of the A-monotonicity, the solvability of a class of nonlinear variational inclusions using the generalized resolvent operator technique is given. The results obtained are general in nature. (c) 20... 详细信息

关键词： A-monotonicity variational inclusion systems resolvent operator technique generalized resolvent operator technique maximal monotone mappings

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：