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A REMARK ON THE DERIVATE OF set-valued mapping

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Journal of Mathematical Study 1994年第1期 51-55页

作者： Chen Bing(Dept. of Math. Jinzhou Teachers CollegeJinzhou 121003)

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关键词： set-valued mapping H-derivate set-valued integral.

Formal Concept Analysis Based on set-valued mapping

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Chinese Quarterly Journal of Mathematics 2008年第3期23卷 390-396页

作者： CHEN Li-ya HUANG Tao SONG Zhen-ming PEI Zheng School of Mathematics Computer Engineering Xihua University Chengdu 610039 China Zheng zhou Industry Safety Vocational College Xinzheng 451192 China Department of Applied Mathematies Southwest Jiaotong University Chengdu 610031 China

Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.

关键词： FCA set-valued mapping isomorphism

A Fixed Point Theorem for set-valued mapping in Abstract Convex Space with Application

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Journal of Mathematical Research and Exposition 2009年第4期29卷 716-720页

作者：范晓冬向淑文 Department of Mathematics Bohai University Department of Mathematics Guizhou University

A new fixed point theorem and the selection property for upper semi-continuous set-valued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-... 详细信息

关键词： set-valued mapping fixed point continuous selection Nash equilibrium.

Natural mappings on set-valued mapping Spaces

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Chinese Quarterly Journal of Mathematics 2011年第1期26卷 21-25页

作者： LI Zu-quan WANG Jiu-jing School of Sciences Hangzhou Normal UniversityHangzhou 310036China Library Hangzhou Normal UniversityHangzhou 310036China

In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.

关键词： set-valued mapping compact-open topology natural mapping

On Ekeland's Variational Principle for set-valued mappings

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Acta Mathematicae Applicatae Sinica 2007年第1期23卷 141-148页

作者： Sheng-jie Li Wen-yan Zhang College of Mathematics and Science Chongqing University Chongqing 400044 China

In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a dosed relation to εk^0 -efficient points of set-valued optimization problems. The main result presented in ... 详细信息

关键词： Vector Ekeland variational principle nonlinear scalarization function metric space set-valued mapping

K-quasi-additive fuzzy integrals of set-valued mappings

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Progress in Natural Science:Materials International 2006年第2期16卷 125-132页

作者： WANG Guijun and LI Xiaoping ( School of Mathematics Science, Tianjin Normal University, Tianjin 300074, China School of Management, Tianjin Normal University, Tianjin 300074, China) School of Mathematics Science Tianjin Normal University Tianjin 300074 China School of Management Tianjin Normal University Tianjin 300074 China

We first define the quasi-addition and quasi-multiplication operations by introducing the inductive operator, and then, in the K-quasi-additive fuzzy measure space, we establish the K-quasi-additive fuzzy integral of a generally measurable set-valued mapping. Applying the integral transformation theorem, some basic properties of the K-quasi-additive fuzzy integrals with respect to this kind of set-valued mapping are studied. Finally, the generalized monotone convergence theorems of this kind of fuzzy integrals are obtained.

关键词： set-valued mapping inductive operator integrable selections K-quasi-additive fuzzy integrals.

Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

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Applied Mathematics and Mechanics(English Edition) 2007年第6期28卷 721-729页

作者：徐海丽郭兴明 Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072P. R. China

An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.

关键词： mixed variational-like inequality three-step iterative algorithm set-valued mapping auxiliary principle technique

Existence and Algorithm of Solutions for Generalized set-valued Strongly Nonlinear Mixed Variational-like Type Inequalities

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Journal of Donghua University(English Edition) 2007年第4期24卷 467-472,477页

作者：胡梦瑜曾六川陈珊敏 Department of Mathematics Shanghai Normal University Department of Applied Mathematics Donghua University

The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.

关键词： iterative algorithm set-valued mapping existence convergence Hilbert space

On Generalized Vector Equilibrium Problems

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Acta Mathematicae Applicatae Sinica 2006年第1期22卷 21-26页

作者： An-hua Wan Jun-yi Fu Wei-hua Mao Department of Applied Mathematics South China Agricultural University Guangzhou 510642 China Department of Mathematics Nanchang University NaIlchang 330047 China

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of... 详细信息

关键词： Vector equilibrium problem set-valued mapping topological vector space KKM theorem