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Alternative principles and minimax inequalities in G-convex spaces

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Applied Mathematics and Mechanics(English Edition) 2008年第5期29卷 665-672页

作者： Mircea Balaj Department of Mathematics University of Oradea410087 OradeaRomania

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems co... 详细信息

关键词： G-convex space strict KKM property fixed point theorem maximal element alternative theorem minimax inequality

GENERALIZED minimax INEQUALITIES AND FIXED POINT THEOREMS

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Applied Mathematics and Mechanics(English Edition) 1991年第5期12卷 493-500页

作者：马意海张福保 Department of Mathematics Xuzhou Teacher's College Xuzhou

Recently many authors have generalized the famous Ky Fan's minimax inequality. In this paper, we put forward T-diagonal convexity (concavity) conditions and develop the main results in this respect. Next, we discuss s... 详细信息

关键词： T-diagonal quasi-concave (-convex) minimax inequality fixed point theorem

A New Fixed Point Theorem in Noncompact L-Convex Metric Spaces with Applications to minimax Inequalities and Saddle Points

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Journal of Mathematical Research and Exposition 2011年第2期31卷 330-336页

作者： Kai Ting WEN Department of Mathematics Bijie University Guizhou 551700 P. R. China

In this paper,a new fixed point theorem is established in noncompact complete Lconvex metric *** applications,a maximal element theorem,a minimax inequality and a saddle point theorem are obtained.

关键词： L-convex metric space fixed point maximal element minimax inequality saddle point

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

Weak KKM theorems in generalized finitely continuous space with applications

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Applied Mathematics and Mechanics(English Edition) 2013年第10期34卷 1291-1296页

作者：方勉王磊 Department of Economic Mathematics South Western University of Finance and Economics

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.

关键词： weak Knaster-Kuratouski-Mazurkiewicz (KKM) mapping generalized finitely continuous space (GFC-space) minimax inequality GFC-quasicovex

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

A parametric type of KKM theorem in FC-spaces with applications

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Applied Mathematics and Mechanics(English Edition) 2009年第1期30卷 73-79页

作者：邓磊臧小燕 School of Mathematics and Statistics Southwest UniversityChongqing 400715 P. R. China

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.

关键词： FC-subspace FC-parametric-quasiconvex mapping minimax inequality

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

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Applied Mathematics and Mechanics(English Edition) 1998年第6期19卷 521-529页

作者：丁协平 Department of Mathematics Sichuan Normal University 610066 Chengdu PR China

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

关键词： mixed nonlinear variational-like inequality minimax inequality auxiliary variational inequality general algorithm reflexive Banach space

SECTION THEOREMS,COINCIDENCE THEOREMS AND INTERSECTION THEOREMS ON H-SPACES WITH APPLICATIONS

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Applied Mathematics and Mechanics(English Edition) 1993年第9期14卷 803-815页

作者： Zhang Shi-sheng Zhang Ying Sichuan University.Chengdu Univ.of Electronics Sci.and Tech.of China Chengdu

The purpose of this paper is to study the section theorems,coincidence theorems and intersection theorems on *** a way of application,we use these results to study the existence problems of solutions for minimax inequalities and variational *** results presented in this paper improve and extend the corresponding results in[1,3,5,6,8,9,12,14,15,17]

关键词： section theorem coincidence theorem intersection theorem,H-KKM mapping variational inequality minimax inequality