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New Generalized R-KKM Type Theorems in General Topological Spaces and Applications

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1869-1880页

作者： xie ping ding College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 P. R. China

In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.

关键词： generalized R-KKM mapping finitely closed-valued (open-valued) generalized R-KKM type theorem minimax inequality saddle point equilibrium problem

System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

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Acta Mathematica Sinica,English Series 2006年第5期22卷 1529-1538页

作者： xie ping ding College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 P. R. China

A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.

关键词： Generalized game System of generalized vector quasi-equilibrium problems KKM property Himmelberg type fixed point theorem Locally FC-space

Existence and Algorithm of Solutions for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces

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Acta Mathematica Sinica,English Series 2012年第3期28卷 503-514页

作者： xie ping ding College of Mathematics and Software Science Sichuan Normal University

Some classes of mixed equilibrium problems and bilevel mixed equilibrium problems are introduced and studied in reflexive Banach spaces. First, by using a minimax inequality, some new existence results of solutions and the behavior of solution set for the mixed equilibrium problems and the bilevel mixed equilibrium problems are proved under suitable assumptions without the coercive conditions. Next, by using auxiliary principle technique, some new iterative algorithms for solving the mixed equilibrium problems and the bilevel mixed equilibrium problems are suggested and analyzed. The strong convergence of the iterative sequences generated by the proposed algorithms is proved under suitable assumptions without the coercive conditions. These results are new and generalize some recent results in this field.

关键词： Mixed equilibrium problem bilevel mixed equilibrium problem monotonicity auxiliary principle iterative algorithm Banach space

Generalized gap functions and error bounds for generalized variational inequalities

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Applied Mathematics and Mechanics(English Edition) 2009年第3期30卷 313-321页

作者：胡艳红宋文 xie-ping ding Department of Mathematics Northeast Normal University Changchun 130024 P. R. China Department of Mathematics Harbin Normal University Harbin 150080 P. R. China 不详

We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

关键词： variational inequality gap functions error bounds

Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces

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Applied Mathematics and Mechanics(English Edition) 2014年第7期35卷 925-934页

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

A new bilevel generalized mixed equilibrium problem （BGMEF） is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.

关键词： generalized mixed equilibrium problem (GMEP) bilevel generalized mixedequilibrium problem (BGMEP) monotonicity minimax inequality topological vectorspace

FC-空间内广义矢量拟平衡问题组解的存在性

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数学学报（中文版） 2009年第5期52卷 919-930页

作者：丁协平四川师范大学数学与软件科学学院成都610066

在没有凸性结构的FC-空间内对集值映像引入了G_i(x)-FC-对角拟凸,C_i(x)- FC-拟凸,和G_i(x)-FC-拟似凸概念,应用这些概念和作者在乘积FC-空间内对一族集值映像得到的极大元存在性定理,在非紧FC-空间内对四类广义矢量拟平衡问题组的解证... 详细信息

在没有凸性结构的FC-空间内对集值映像引入了G_i(x)-FC-对角拟凸,C_i(x)- FC-拟凸,和G_i(x)-FC-拟似凸概念,应用这些概念和作者在乘积FC-空间内对一族集值映像得到的极大元存在性定理,在非紧FC-空间内对四类广义矢量拟平衡问题组的解证明了某些新的存在性定理。这些定理改进和推广了文献中的某些最近的已知结果到非紧FC-空间。

关键词：极大元广义矢量拟平衡问题组 FC-包

广义凸空间内的KKM型定理和极小极大不等式及鞍点定理

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数学学报（中文版） 2004年第4期47卷 711-722页

作者：丁协平四川师范大学数学与软件科学学院成都610066

本文在非紧G-凸空间内对具有有限闭值和有限开值的G-KKM,广义G-KKM和广义S-KKM映象建立了某些新的KKM型定理。应用这些KKM型定理,在G-凸空间内得到了新的 Ky Fan型极小极大不等式和鞍点定理。这些结论推广了最近文献中的许多已有结果。

关键词： G-KKM型定理极小极大不等式鞍点

QUASI-EQUILIBRIUM PROBLEMS AND CONSTRAINED MULTIOBJECTIVE GAMES IN GENERALIZED CONVEX SPACE

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Applied Mathematics and Mechanics(English Edition) 2001年第2期22卷 160-172页

作者： ding xie-ping(丁协平) Department of Mathematics Sichuan Normal UniversityChengdu 610066 P R China

A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, ar applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify, and generalize the corresponding results of the multiobjective games in recent literatures.

关键词： quasi-equilibrium problem constrained multiobjective game weighted Nash-equilibria Pareto equilibria generalized convex space

Modular assembly of complex C-alkyl glycoside enabled via cooperative NHC and photoredox catalysis

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Science China Chemistry 2025年

作者： Rui-Qiang Jiao Ming Li Xi Chen Mei-Ze Xu Tian ding Xiao-ping Gong Zhuo-Mei Li Xue-Yuan Liu Yong-Min Liang State Key Laboratory of Applied Organic Chemistry Lanzhou University College of Chemistry and Chemical Engineering Northwest Normal University

C-Alkyl glycosides are found in natural products and are indispensable in drug development programs,owing to their diverse range of medicinal ***-component reactions involving glycosyl radical addition are well documented and proved efficient for the C-alkyl glycosides ***,multicomponent reactions for the rapid and controllable construction of structurally diversified C-alkyl glycosides in a single step remains a significant challenge due to the issues associated with balancing reactivity,compatibility,and ***,we report an NHC and photoredox co-catalyzed three-component method to access complex and valuable C-alkyl *** protocol exhibits broad substrate scope and excellent chemoand ***,nine types of sugars are compatible with this *** addition,the generality of this catalytic strategy was further highlighted by the potential for scalable production,the feasibility of further modifications of the products and its successful application in the late-stage functionalization of pharmaceutical skeletons.

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