KKM技巧及其应用

张石生; 马意海

KKM技巧及其应用

张石生¹,
马意海²

1.
四川大学数学系;
2.
徐州师范学院

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- 被引次数: 0
出版历程
- 收稿日期: 1991-11-06
- 刊出日期: 1993-01-15

KKM Technique and Its Applications

Zhang Shi-sheng¹,
Ma Yi-hai²

1.
Department of Mathematics. Sichuan University, Chengdu;
2.
Department of Mathematics Xuzhou Teacher' College, Xuzhou

摘要

摘要: 本文介绍KKM技巧,并用以建立了新的抉择定理和重合定理,它们是[2,10,11,15,16]等近期文献中一些重要结果的推广.
- H-空间 /
- KKM映象 /
- 抉择定理 /
- 重合定理
Abstract: In this paper, the Knaster-Kitrattnvski-Maiurkiewic: technique(KKM technique, in short) is presented. By using this technique a new alternative theorem ami a new coincidence theorem are estahlished. The results obtained in this paper unify and generalize the corresponding results in the recent works^{[2,10,11,15,16]}.
- H-space /
- KKM mapping /
- alternative theorem /
- coincidence theorem

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参考文献(16)

[1]	Baiocchi,C.and A.Capelo,Variational and Quasi-variational Inequalities,John Wiley and Sons(1984).
[2]	Bardaro,C.and R.Ceppitelli,Applications of the generalized Knaster-Kuratowski-Mazurkiewiez theorem to variational inequalities,J.Math.Anal.Appl.,137(1989),46-58.
[3]	Browder,F,E.,The fixed point theory of multivalued mappings in topological vector spaces,Math.Ann.,177(1968),283-301.
[4]	Chang Shih-sen and Chang Yin,Generalized KKM theorem and variational inequalities,J.Math.Anal.Appl.(in print).
[5]	Dugundji,J.and A.Granas,Fixed Point Theory,Vol.Ⅱ,Warszawa(1982).
[6]	Fan,K.,A generalization of Tychonoffs fixed point theorem,Math.Ann.142(1961),305-310.
[7]	Fan,K.,Some properties of convex sets related to fixed point theorems,Math.Ann.,266(1984),519-537.
[8]	Granas,A.,KKM-maps and their applications to nonlinear problems,The Scottish Book(Mathematics from Scottish Cafe),Edited by R.D.Mauldin,Birkhäuser,Boston(1982).
[9]	Ha,C:-W.,On a minimax inequality of Ky Fan,Proc.Amer.Math.Soc.,99,4(1987),680-682.
[10]	Horvath,C.,Some results on multivalued mappings and inequalities without convexity,Nonlinear and Convex Analysis,Lecture Notes in Pure and Appl.Math.,Series 107(1987).
[11]	Jiang Jia-he,Coincidence theorems and minimax theorems,Acta Mathematica Sinica,New Series,5,4(1989),307-320.
[12]	Knaster,B.,K.Kuratowski and S.Mazurkiewicz,Ein Beweis des Fixpunktsatzes fur n-dimensionale Simplexe,Fund.Math.,14(1929),132-137.
[13]	Lassonde,M.,On the use of KKM multifunctions in fixed point theory and related topics,J.Math.Anal.Appl.,97(1983),151-201.
[14]	Mazur,S.and J.Schauder,Über ein Prinzip in der Variationsrechnung,Proc.Int.Congress Math.,10(1936),65.
[15]	Park,S.,Generalizations of Ky Fan's matching theorems and their applications,J.Math.Anal.Appl.,141(1989),164-176.
[16]	Shih,M.-H.and K.-K.Tan,A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems,J.Austral.Math.Soc.,Series A,45(1988),169-183.