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maximal elementS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

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Applied Mathematics and Mechanics(English Edition) 2003年第6期24卷 1017-1024页

作者：丁协平 Department of Mathematics Sichuan Normal University

A new family of set_valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set_valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature.

关键词： maximal element family of G B_ majorized mappings product G_ convex space

maximal elementS OF A FAMILY OF G_B-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

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Applied Mathematics and Mechanics(English Edition) 2006年第12期27卷 1607-1618页

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

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

关键词： maximal element family of GB-majorized mappings fixed point system of minimax inequalities product FC-space

maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

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Applied Mathematics and Mechanics(English Edition) 2007年第12期28卷 1561-1568页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University

First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

关键词： condensing set-valued mapping maximal element generalized game equi-librium locally FC-uniform spaces

AN EXISTENCE THEOREM FOR maximal elementS AND ITS APPLICATIONS

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Applied Mathematics(A Journal of Chinese Universities) 2007年第2期22卷 235-244页

作者： Hou Jicheng He Wei Department of Mathematics Beijing Information Technology Institute Beijing 100101 China Department of Mathematics Nanjing Normal University Nanjing 210097 China

An existence theorem of maximal elements for an L＊-majorized correspondence defined on a non-paracompact H-space is established. As applications of the result, an equilibrium existence theorem for a non-paracompact g... 详细信息

关键词： maximal element generalized game equilibrium H-space,L*-majorized correspondence

Special Relationship among Decision Making Units based on Partially Ordered Set and New Evaluation and Projection Methods

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Journal of Systems Science and Systems Engineering 2022年第2期31卷 226-246页

作者： Muren Chang Liu Wei Cui Jinquan Dong School of Statistics Jilin University of Finance and EconomicsChangchun130117China bSchool of Management Science and Information Enginering Jilin University of Finance and EconomicsChangchun130117China cSchool of Economic and Management Inner Mongolia University of TechnologyHohhot010051China

This paper provides data envelopment analysis methods based on partially ordered set *** methods reveal the special relationships between two decision making units from the perspective of mathematical theory and offer the classification,projection and improvement methods of decision making *** is proved that an efficient decision making unit must be a maximal element of the related poset,and the maximal element may not be *** this,we introduce the concepts of minimum envelope and efficiency envelope which further reveal the special relationship among efficient and inefficient decision making *** with the previous methods,this method not only reveals theoretically the complex relationship among decision making units and the causes of the ineffectiveness,but also gives a new importance and competitiveness measurement method to each decision making ***,related algorithm and examples are given for the application of these methods to complex decision making problems.

关键词： Data envelopment analysis partially ordered set returns to scale projection maximal element

GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

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Acta Mathematica Scientia 2020年第6期40卷 1849-1873页

作者： H.SHAHRIARIPOUR H.MOHEBI Department of Mathematics Graduate University of Advanced TechnologyKermanIran Department of Mathematics and Mahani Mathematical Research Center Shahid Bahonar University of KermanP.O.Box:76169133Postal Code:***KermanIran

The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well *** this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space *** also study,for this class of functions,some concepts of abstract convexity,such as support sets and ***,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

关键词： increasing plus-convex-along-rays function support set maximal element global minimum DC-function

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

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Acta Mathematica Scientia 2010年第4期30卷 1257-1268页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University Chengdu

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

关键词： maximal element system of generalized vector quasi-equilibrium problems Mathematical program Ci(x)-FC-partially diagonally quasiconvex Ci(x)-FC-quasiconvex Ci(x)-FC-quasiconvex-like FC-space

NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

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Acta Mathematica Scientia 2011年第3期31卷 1142-1154页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity *** applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

关键词： maximal element system of generalized quasi-variational inclusion problems system of quasi-optimization problems mathematical programs with systems of generalized quasi-variational inclusion constraints F C-space

Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces

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Applied Mathematics and Mechanics(English Edition) 2010年第5期31卷 545-556页

作者：丁协平 College of Mathematics and Software Science Sichuan Normal University

By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion （disclusion） problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

关键词： maximal element system of generalized quasi-variational inclusion (disclusion) problems partially diagonally quasi-convex partially diagonally quasi-concave,FC-space